A contactor is essentially a big relay, however they're far more robust. The main benefit of a contactor is it should never fail to disconnect due to welded contacts. They physically move a link bar between each terminal, so if one contact should stick, the stronger spring will still disconnect the opposite end, whereas a relay only has one contact.
Contactors generally use more power, due to the stronger spring.

Officially, the e-stop should use a max of 24V, which then controls the main power via a relay/contactor.

SSRs are an option, but aren't ideal for e-stop circuits as they can fail closed if overloade.