Oh yeah, i thought the previous user used them interchangeably. I messed it up. I think it's exclusive in a way that no one else could make the same deal. Not explicitly locking others out, but in a significant way, it implicitly did.

The point was they became a monopoly cos they had a good product, and now the product is not as good after these default deals they made with Apple, Samsung etc.

It is exclusivity. I've been involved in some of these contracts going all the way back to the Summer of 2004 and they absolutely involve exclusivity. If Safari or Firefox product managers added a new search access point and their business people tried to sell default placement for that new search access point, they'd violate their contract. That's exclusivity. Opera used to do that kind of thing, they had three different search defaults for three different access points in the 2000s but by 2010 Google was no longer allowing that in their contracts because exclusivity.

That might just be overloading the term in a way that clouds the issue though? The exclusive default search provider for a browser vs the exclusive search provider for a browser is pretty different.