A dove-tail is typically found on .22LR rifles. It's a narrow rail with no cross-slots.
Typical Weaver Rail
A Weaver rail is a wider rail with cross-slots placed wherever convenient, and usually just enough of them to mount a standard scope with two rings.
A Mil-Std 1913 (aka "Picatinny") rail is essentially a standardized Weaver rail. The size, depth, and spacing of the cross-slots is rigidly defined, as is the width and angle of the rail cuts. This allows all kinds of devices to be designed that can be moved from one gun to another without changing the mounts.
All but the earliest AR flattops have 1913 rails, as do the modern railed forends, such as the KAC RIS/RAS, ARMS SIR, and so forth.