This is the fundamental starting point. While the terms are sometimes used interchangeably, they refer to two distinct components:
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Scope Base: This is the part that attaches directly to the receiver of your rifle. It is the foundation. Bases are typically one of two styles: a Picatinny Rail (a continuous rail with multiple slots for maximum flexibility) or a set of Weaver-style bases (usually two separate bases screwed into the receiver).
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Scope Mount: This is the assembly that connects your optic to the base. The most common types are Rings (which clamp onto a rail base) and a One-Piece Mount (a single unit that combines the base and rings into one solid piece).
In short: the base is on the gun, and the mount (or rings) holds the scope and attaches to the base.