It looks to me like both definitions are widely used. The first paragraph on Wikipedia claims that the term "hard sci-fi" was coined first, then "soft science fiction" was coined specifically to make the distinction between hard science and soft science. That paragraph also notes that there is no rigorous distinction, and mentions Foundation as a classic example.
I strongly disagree, I don't think the "soft-science fiction" and "hard-science fiction" meanings are widely used; if you use these meanings often then you'll probaby very frequently cause confusion and prompt discussions like this one. Almost everybody is using the other meanings, at least in recent years.
