Most standard contacts simply change state.
In general every OL relay has at least 1 contact which is consider Normally Closed (it is closed when there is no overload). This contact opens on an OL trip thus breaking the coil circuit.
IEC overload relays almost always come with an additional contact which is Normaly Open and then closes when a trip occurs, this is often called an alarm contact. This second contact is usually an adder for NEMA starters. It is typical for this contact to share a common terminal with the NC contact.
Of course there are exceptions such as (2) open contacts or contacts with isolated terminals.