What is a species and a transitional species?

In general, I am interested in the terminology and framework of evolutionary theories for my own purposes. For example, “species.” Does it have a life cycle like: - origin of a species - a clearly expressed transitional stage of this species - stable phase - increasingly narrow “specialization” (if such exists) Is there a difference between endemic species and others? And in general, does a “transitional species” and a “stable species” exist, or is any biological species at any given moment in a process of continuous change, being a “transitional species” between itself yesterday and itself tomorrow?