A language confusion

I was recently at a con where there was a group discussion about strap-ons, and people kept talking about topping and bottoming. This threw me a little, because it didn't seem to match the BDSM terminology I've been used to - where the top is someone with more control, I guess? What really threw me was when Iwas asking whether someone can top while lying down on their back and someone else is on top of them, and it caused much confusion!

So now I'm wondering about terminology. Have I got it right? Who's the top and who's the bottom in BDSM and in strapping on?