Ok, so I've been on Facebook for years. Recently got a bit bored with it, but that's beside the point.
At work a couple of months ago, I was experimenting with OAuth/OpenId, and tried to set up a 'log in with Facebook' feature (along with Google, Twitter, etc).
I decided that I didn't want to associate my work with my existing Facebook account, so I created a brand new Facebook account, with my work email. The only thing that was common between the two accounts was my name (which isn't exactly the most unique in the world).
Was debugging an issue today, and had to log into my work Facebook account to check the app settings - and was a little surprised to see a list of 'Friends you might know', and they were actually people that I do know.
Maybe I screwed up somewhere and logged in with the wrong account once, but I'm pretty sure I didn't.
Part of me is impressed that it actually has worked out who I know (or at least made a connection between the two accounts), but the rest of me just doesn't like it.
My guess is that I accidentally signed in to the app with my personal account once, and is picking up a relationship that way. If that's the case, then fine, I get it. If not, then I have no idea what's going on.
You were probably working from the same computer with the same IP address and the previous cookies for your other FB account. I don't know how much they track but knowing the same member computer is creating a new FB account is trivial to track if you don't start with a fresh slate of cookies.
That's why I use separate browsers for my various FB and Twitter accounts so they can't be accidentally cross associated in any way shape or form. Firefox is my primary, then I use MSIE and Chrome for two others, and Opera for another rarely used account, etc.
If I wanted to be even stealthier I'd set up each browser with a proxy IP or use a TOR proxy to guarantee no chance of cross contamination but so far the individual browser trick seems to work well enough on it's own.