First, the same type of chord will sound similar across keys regardless of what type it is. Major, minor, 7, whatever. The quality of a chord comes from both the specific notes used and the intervals between them, and the latter is the same regardless of key.
Second, the 7 chord is often used for a very specific purpose: to lead into another chord. This gives it a very distinct and easily recognized color.
Let’s say you’re in the key of C major. You’re about to end the song and want to indicate that you’re about to return to C major, but create one last bit of tension before you get there. A G7 chord is not a C major chord, but it clearly indicates that you are in the key of C major, because no other major key includes all 4 of those notes. So you use that chord to lead back to it.
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