Is there any difference between 'to affiliate with' and 'to affiliate to'?

When I was looking up the word ‘affiliate‘, the dictionary offered the example sentences which I’ve been really confused from.

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The actual meaning of the word ‘affiliate’ is

• to cause a group to become part of OR form a close relationship with another, usually larger, group, or oganization.

Now, which sentence applies to which meaning?

1. A ​college affiliated to the University of Mumbai.
2. The ​school is affiliated with a ​national ​association of ​driving
   schools.

I assume that the first sentence means that 2 schools have associated so now, they work as a whole and the second one refers to the fact, that these 2 companies have just a good relationship that helps them to be both more profitable. Am I right?