i think it's a different kind of pain. if it's similar to how you feel when you tier your legs, then go up/down stairs, then it's muscle. if it hurts when your tork it, or feel sharp, pinchy, or radiates, (there's other sorts that could be hurt too, but i can't think of them) then it's probably hurt back.
that said, you're really the only one who knows your body and what those feel like.... so i hope that helps, but don't take it too seriously.
either way, you PROBABLY don't want to let it tense up. (not sure what might have happened, if rest might be better, but when i pull something there, i usually think heat and want to just lay there, when i need to stretch and ice it. stupid back packs.... so many reasons i dont use them anymore!)

I did some pilates short back – or long back, I never know the difference – and some mild ab work last night, and it seems to be better. So I guess it was more of a strength issue than a hurt issue.

It was just odd, having an ache in a different place than where my back normally hurts, when it hurts.

If massage helps ease it, then it's probably normal muscle soreness.

I usually find it reasonably simple, if it goes away in a day or so, it's probably just natural muscle soreness. If not you've hurt your back, go to the doctor.