Anything that switches arcs.
Technically a contactor is just another name for a relay, however the term contactor has been adopted to describe a specific type of relay.

Contactors main benefit is they can handle far higher currents, and normally have a pretty large airgap to ensure a well isolated disconnection. There's no real reason to use a contactor unless the application dictates it, especially if you can get away with a far cheaper relay.
I'm pretty sure you can get contactor set-ups that will detect a welded contact, which essentially gives you the equivalent of a positive guided relay. All you need to do with a contactor is monitor the contact plate travel, so it's just a case of actuating a suitable switch to detect that it's not returned fully. However if you've just welded a contactor shut, then there's a major design flaw somewhere!