These are two tricky words because it seems that concept and conception can be used interchangeably. They are releated to each other in a sense that both refers to creating or having something new.
Conception is the act of conceiving things and persons. Conception referes to how a new organizm is produced. This word is used synonimously to fertilization.
A concept is a notion or an idea, very often referring to a new one. It is often an abstraction or generalization from experience or from theory.
In the law, concepts referes to legal rules connected to and regulating a particular situation which is addressed specifically by the legal system. Easement, for instance, is a legal concept related to using the land of another in a certain way.
In summary, the difference between the two is that a concept is somewhat similar to a thought or an idea, whereas conception is the act of conceiving, i.e. having or producing a concept