ELI5: Why do we recognize that mirrors are "silver" when they appear to be the exact same color as what they are reflecting?

Not all mirrors are perfectly reflective, and things can be done to a mirror to make it less reflective (like fogging, smudging, etc).

If you look at something like the side of a butter knife, you can see that it has a color, despite also reflecting the world around it. If you polish the side of that knife enough, eventually you’d get a usable mirror.

Common household mirrors are a thin layout of silver on the back of a pane of glass, so their color when less than perfectly reflective is the same as the color of unpolished silver.

As had been pointed out, modern mirrors use aluminum, since it is almost as good but a lot cheaper. Still, the language evolved in a time when aluminum was less common.

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