Even if symlink is more often used I think softlink is the official term.
Now vice vesa. In Mention of Kevin Vermeer posting I exchanged the two tags. I didn't checked which term is more common.
Symlink, short for symbolic link, is the official terminology according to the POSIX specification:
I'd never heard of a softlink until today. It seems to be the logical opposite of a hard link (which would be 'soft link', which ought to result in the tag soft-link, right?), but the official name on Linux, Mac, and Windows for these files is symlink.
I note that the Wikipedia article does mention soft links:
but it only does this in the introduction, in the reference to the Amiga OS (where they are called soft links), and in a reference to what I can only assume is a misguided Linux tutorial.
Additionally, there are 338 questions tagged symlink, and 10 questions tagged softlink. There is already a synonym mapping symbolic-link to symlink. I could support mapping softlink to symlink, but not the other direction.