Yes, Plaid clearly has different levels of integration with different banks.

When I connect something to Chase with Plaid it is clearly a cooperative system with an OAuth-like permission dialog, and the Chase side even mentions they're tokenizing the account numbers so Plaid can't see them.

When I connect to the little bank down the street I just get a username/password dialog. Their web banking system is so primitive I'm pretty sure Plaid is just scraping it. When they introduced 2FA, Plaid became quite flaky.