Well a pinned barrel means there is a pin that protudes above the barrel in the top of the frame and recessed means the cylinders are counter bored so that the whole bullet case including the rim fits inside the chamber. On a non recessed cylinder the case rims sit outside the chamber and are against the cylinder face and can be seen when you look at the revolver when the cylinder is closed.

Check the side pay by gently turning the cylinder in the revolver when the cylinder is closed and some is normal but a lot is not. Also check this when the hammer is cocked because that is when lockup is critical.

Someone else can discuss end play but it's basically the cylinder moves up and down instead of in a rotational movement when closed.

Picture of a revolver with pinned barrel