Learn English – “greetings programs”

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.

A "public worker" is someone who works for the government. It would include teachers at public schools (i.e. government-run schools), policemen, bureaucrats, etc.

"Public works" means government-run construction projects. So a public worker might well be involved in public works, but they also could be doing many other things.

I should clarify that this is American usage. I don't know if it's different in other English-speaking countries. I think it's the sort of word that might be.