I think the real difference is that "commonplace" is not just ordinary, but has a feeling of blandness and lacking individuality added to it. "Common"= merely suggests that it is widely available (but I don't think it suggests blandness like the word commonplace does)

We use the word "common" all the time. It's basic vocabulary. It means something that happens frequently, or something normal, or something almost everybody does. "Where I live, snow is common in the winter. Therefore, it is common to own a snowblower." "Commonplace" is used much less often. As a learner, it is not a word you will need to use yourself. We would be more likely to say "everyday" or "ordinary." According to one online source, "common" is among the 1,000 most frequently used words, and occurred at least ten times as often as "commonplace." In US English it is slightly literary or old-fashioned. "Commonplace" always carries a sense of being boring. It is something automatic, or uninteresting. It does not draw your attention. You do not think about it much.

Well common has a couple of meanings, 1) a common thing is something that you can find often, 2) a common thing is something that a group of people own. commonplace basically means 1). But it is seldom used by most people. I'd avoid.