What is the difference between continuous supported edge and simply supported edge of a slab?

First of all, understand how concrete structures are built. Rebar is laid and concrete is poured. Everything is joined together with little separation. This is what we call “continuous” and is normally the case for concrete. If there is some separation, like a gap or a hinge, it is “simply supported.”

A “continuous” structural component does not carry 100% of its own load. Some load will be shed into a nearby component. It goes to say that a “simply supported” slab will carry more load (wL^2/8 in the case of a uniformly loaded floor slab) than the same “continuous” slab.

This all might more sense if you are familiar with influence lines. If bending in one span of slab can also create bending in the adjacent slab, they are continuous/together at that edge. If bending in one span of slab does not create bending in the adjacent slab, it is simply supported at that edge.