Learn English – Difference between “Watch you head” and “Mind your head”

Install means to put a program on your computer. Setup can mean to configure the program, including various options, as in:

I'm going to set up Word so that the grammar checker is turned off.

I would say that when you are installing a program, you are also performing its initial setup, so either word could be used in that context. Put another way, you can set up a program after it's been installed, but you can't install a program after it's been set up.

By the way, there seems to be a slight logic flaw in the wording of your question. You said:

According to Wikipedia, setup directly means install on computer:

Installation (or setup) of a computer program...

I wouldn't say that the parenthetical "(or setup)" after the word "Installation" indicates that "setup directly means install". "Directly means" seems too strong an interpretaion for language. Instead, I would say:

According to Wikipedia, setup is another word for install:

Installation (or setup) of a computer program...

The difference is slight, but subtle. My wording implies that, when installing a program, you could also use the word setup – but setup may have other meanings as well. Your wording seems to imply that setup is more of an exact synonym, with no other meanings.

I'd diagram the difference like this:

Put another way, I wouldn't say:

The word right directly means correct.

because the word right, in addition to being the opposite of wrong, can also mean the opposite of left, or describe a 90-degree angle. That's why I'd say something more like:

The word right can be used to mean correct.

In this case, I would say:

The word setup can be used to mean install.

which is an accurate statement, and aligns with what you found in Wikipedia.

There is no difference in meaning; there is an enormous difference in use.

Many languages have grammaticalized systems of deference, which encode a variety of differences in social standing between the participants in a conversation. Britons (who never never ne-ver shall be slaves) and Americans (whose Charter Myth is that all men are created equal) scorn these ways of speaking as repulsive toadying; but we have equally elaborate codes for acknowledging and regretting the unhappy necessity of imposing burdens on our peers.

For instance: it would be unspeakably peremptory to require that your interlocutor “Give me an answer at once!” Even your own more gracious “I await your reply as soon as possible” suggests to us a frigid insistence on your own needs, only slightly tempered by a condescending indication that your impatience will, if it must, tolerate some slight delay.

(We all know that that’s not what you mean; but it’s what it would mean if a native speaker said it.)

In the same way, “What time is it?” is an abrupt demand for information; it would be acceptable only in a situation of extreme urgency or between people with an established close personal or professional relationship. With a stranger you must be more hesitant and less willing to impose; you must make it clear that you value his time no less highly than he does, that you regret the necessity of intruding upon his attention, and that you do not even go so far as to request, however humbly, the information you require: you only wonder, hypothetically, whether it is possible that he might unbend so far as to consider, hypothetically, providing it.