apply for/ apply to/ application for

Hi, I am a little confused over the use of the word “apply”. Are the three uses of “apply” correct?

application for an university
apply for a job
apply to an university

Also, what is the difference between “apply for something” and “apply to something”?

Thank you for your clarification.

Xiaoxuan

You apply to a person or institution.
You have the uses correct.

Yes, you apply to a person or institution, and you apply for something.
So, do you actually mean your first statement?
Further, more importantly, note that it is A UNIVERSITY.

Apply for a institution
and apply to a university
are both possible.

In the second cade you apply to the institution.
The first one is a shortened way of saying 'Applied for (a place at) a university.

Oh, I see. Thanks.

Now I got it.

apply to a person/ an institution, such as a university
apply for something, such as a job
application for a university means “applied for a place at a university”

Many thanks to you guys!