Not always, I have different accounts at the same bank...2 of those accounts can ONLY be accessed by my banks ATM's at the branches, going to just any atm will NOT work. Seeing when we moved there are no branches up here, well, I'd be pretty much SOL, The nearest branch is over an hour away The card? Is a visa/atm card. All of their accounts are like that of this particular kind it's not anything "special" abut my personal account, and yes, the accounts are considered "checking" accounts.
I should have said EVERY card with a Plus, NYCE, Star, Cirrus, etc. logo on the back can be used at ANY ATM.