Difference between "admit" and "accept"

They can both mean the same thing but "admitted" is usually paired with "to":

She has been admitted to York University.

"Accepted" can work with many different prepositions but in this context the most appropriate would be:

She has been accepted into York University.

She has been accepted to York University.

She has been accepted at York University.

The relevant word definitions, by the way:

admit — to allow to enter; grant or afford entrance to: "to admit a student to college."

accept — To admit to a group, organization, or place: "accepted me as a new member of the club."

To me, this is a matter of nuance. In the US, being accepted by a university is pretty much the same as being admitted to one.

But, if someone told me they were accepted, I might ask when they'll be going. And they might respond that they were admitted for the Fall Quarter.

Here, I see accept as: to receive with approval or favor. Admit is to permit, give access to or egress to.