Yeah, those descriptions as they stand now do suggest it's one and the same thing, and that should be corrected. They're not really the same though, launch pad is but one of the many launch site facilities. So I'm inclined to think that both tags should stay, they're not even synonymous in the sense of this site's use, but the launchpad tag does need a better description to make it stand out.
I edited the launchpad tag to now read:
Questions regarding vertical rocket launch platforms and facilities in
their immediate vicinity supporting final preparations for a rocket
It could still use a clearer description, this is just a fast attempt at making it distinct from launch-site.