The following are mostly synonymous and can be translated as "to agree on sth." in the sense of "to reach/come to an agreement", i.e. two or more parties had some kind of conflict/discussion/negotioation which they are resolving.
sich einigen / sich einig werden
sich auf etwas verständigen
The result - the sth. that the parties agree upon - may (but does not need to be) written down as a treaty/contract
has some overlap with this meaning, but it is usually used when the involved parties are discussing how to coordinate efforts on something.
is different - by itself it does not say anything about the process of reaching an agreement, it merely states that the subject agrees to/concurs with something now, no matter if they always did so or were recently convinced.