From the way they tackle problems when discussing.
I have previously written more answers on this. Here are some ways in which more intelligent people think:
1. Symbolic thought
The simplest sign of intelligence is being able to clearly tell what is literal and what is symbolic or metaphorical, and be able to discuss about that concept without necessarily being involved in it.
In the words of the Ancient Greek philosopher Aristotle
It is the mark of an educated mind to be able to entertain a thought without accepting it
Here is one more subtle application of this in everyday life:
If you refer to nuclear physics to less intelligent people, they will think that you are a nuclear physicist. Conversely, they will be having trouble understanding how it is possible to talk about nuclear physics if you are not a nuclear physicist. And they think same with specialised subjects like medicine, law, or business. Well, it has been happening like this since he beginning of mankind. Less intelligent people cannot do it due to their personal limitations.
An exploitation of this cognitive deficiency is partly what famously allowed Frank Abagnale to impersonate doctors, pilots, lawyers, and other people of profession, by simply talking and behaving like them. Other people thought that because he acted like the professionals he imitated, he was one, and could not ever imagine the opposite.
In is even possible that this is inability is behind the success of what is called “social engineering”
I would argue however that this ability is not the product of education, but mostly an innate, genetic ability related to intelligence. It may have just happened that those who were educated in Ancient Greece were only the most intelligent, likely happening through some selection process.
2. Two way relationships
More intelligent people do not understand two way relationships. Here is a question:
If you are a basketball player, you are likely taller than average. If you are taller than average, are you likely a basketball player?
Some people would connect one to the other. In reality, they are different concepts. Mistakes like this are so common not only in everyday thinking, but even in scientifically validated articles and high level business talks.
3. Cause and effect
There is a cause of happenings. Less intelligent people cannot think in terms of cause-and-effect, and this again seems to be a genetic deficiency. Interestingly, it just happens that many people who support left-orientated political parties do not have this ability at all.
Cause-and-effect is about determining what caused something, as well as what did not. The common mistake less intelligent people make is to consider correlations as causal relationships.
Anything can be correlated to something else, by default. This does not mean that one causes the other. Even if they do, there is a chain of events. This type of mistake is also known as “correlation is not causation”. Here is one example:
Being good at this skill, particularly understanding cause and effect in complex scenarios, is fundamental for understanding chain reactions, including chemical reactions, including those happening in the brain, such as how neurotransmitters are produced, as well as how food is broken down etc.
4. Complex, Multiaxiomatic logic
A logical syllogism begins with an axiom, and uses logical methods such as induction, deduction and abduction in order to bring further conclusions, which are said to logically follow from their premises.
The ability to make logical syllogisms is also genetic and built into some people’s way of processing information.
People of low intelligence hardly make basic logical syllogisms. People of average intelligence make logical syllogisms based on some axioms, and apply the logical method correctly.
People of high intelligence can make logical syllogisms, but also take into account the limitations of logic. They know that the results depend on the premises and ultimately the axioms. Very often logic is used incorrectly by intelligent people as its roots are personal axioms. In other words, the fact that something is logical not only does not mean that the conclusion is valid. It can be extremely biased, and even false within the current context.
5. Multi-valued logic
This can be seen from 
the number of conclusions when evaluating a statement:
Less intelligent people use 2 conclusions: True or False
More intelligent people use 3 conclusions: True, False, Unknown
When less intelligent (note re edit: “Smart” does not need to be capatalized, also redundancy of terminology in research writing provides clarity for the reader and is preferred amongst academics) people don’t know about something, they treat it as False. However, using 3 instead of 2 conclusions makes all thought frameworks much richer, precise and valid, but also much more complex.
From the original observation, it could be assumed that less intelligent people can only understand and use binary logic in their thought process, but more intelligent people can understand and use ternary logic, or even higher order n-ary logic. Three-valued logic - Wikipedia
This phenomenon is probably very related to confidence and the Dunning-Kruger effect.
6. Interpersonal intelligence
Interpersonal intelligence is
To understand intersubjectivity, be able to differentiate between the individual participants in the cognitive conversation, and the role and actions of each. Effectively present the interaction as it happened, avoiding what I call ”interpersonal fallacies”.
Interpersonal fallacies are fallacies which happen when people confuse the actors, roles and opinions in a conversation. Typical examples are thinking that what one says is what the other also thinks, getting confused in the exchange of I and You, and ignoring the subjectivity of the observations of the actors.
The more actors are considered in a cognitive conversation, the number of true and false statements, situations and scenarios increases exponentially. A less intelligent person doesn’t have the capacity to perceive enough distinct actors acting simultaneously due to such cognitive incapacities.
For example, a less intelligent person may perceive that when they talk with another, there is them (an I), the other participant (a You), and perhaps a third person (an Other) as all the actors in the conversation.
For a more intelligent person there are many more independent actors perceived in the same conversation above: I, what I think You are, what I think the Other is, what You think You are, what You think I am, what You think the Other is, and so on.
Multiply the number of actors by their actions to see how significantly more complex it is thinking in the latter way.
It is a different type of intelligence which is also calculatable and testable. I am the first person to define this type of intelligence, and the inventor of this type of psychometric assessment.
7. Quantifiability vs Generalisation
This is possibly what makes the cut between intelligent people and highly intelligent people.
Here is an example of generalisation: “All men are chauvinistic pigs”. This sentence is false by definition. A more quantified version could be “30% of men are chauvinists”, ideally backed by correct data.
The true sign of skill in this area is shown when asking someone a question like those previously asked by Google on hiring interviews:
- “How many piano tuners are there in the entire world?”
- “How many vacuums are made per year in the US?”
- “How many golf balls can fit in a school bus?”
Most people will immediately react to these questions as “they are unanswerable”. They are not, and there is even a method to answer them, which highly intelligent people in certain areas can do automatically.
8. Purpose and Gain
This was brilliantly described by Italian economist Carlo M. Cipolla in his essay “The Basic Laws of stupidity” . It is such a defining factor for intelligence, that could even call for a redefinition of the word.
Here is a diagram from this essay:
Intelligence is often described as “the processing and collection of information”. There is a problem with this definition in that doing exactly as it states can lead not only to useless results, but actually be destructive for the performer and others.
The reason is that purpose and gain are missing.
Why process and why collect information? And most of all, what is there to gain for the person who does it? A person who works hard doing things that are not giving themselves benefit, and even worse causing them losses, is _______ (I recommend this verbiage: lacks foresight or lacks situational awareness) [These statements are more empirical]
Too many people have not realised that they are doing this. Intelligent people, and particularly executives, always think of how they can gain from what they do, and ideally how others will gain too.
(This is well written and well supported. You appear to be a subject matter expert. I recommend fleshing out your section on logic and tying up your missives with a formal conclusion, then submitting to academic journals if you are so inclined)