I think the best way to go about remembering these 3 types are by breaking down the name itself. Apical derives from apex, which can refer to the farthest edge or tip of something (roots and stem tips). Lateral is a direction of movement, usually side to side (increased thickness). Intercalary refers to being inserted between other parts, areas/places, or things, in this case between leaf blades and nodes. Hope this helps.

Would it be safe to think of this as a plant version of stem cells since they are undifferentiated?

A very interesting and ancient group of plants.

I've also heard of gymnosperms being refered to as "naked seeded" plants since their seeds are open to air.

A leaflet is a component of a compound leaf resembling an individual leaf. Each of the leaflets and the central midrib pictured actually comprise one leaf of the locust tree.