In lang=en terms the difference between coerce and exploit

is that coerce is to use force, threat, fraud, or intimidation in attempt to compel one to act against his will while exploit is to use for one’s own advantage.

In computing|lang=en terms the difference between coerce and exploit

is that coerce is (computing) to force an attribute, normally of a data type, to take on the attribute of another data type while exploit is (computing) a program or technique that exploits a vulnerability in other software.

As verbs the difference between coerce and exploit

is that coerce is to restrain by force, especially by law or authority; to repress; to curb while exploit is to use for one’s own advantage.

As a noun exploit is

a heroic or extraordinary deed.