Thanks, all, for your answers and for the links. I learned a lot from them - mostly that there was a lot more to know than I realized!
I assumed all tires started out the same. Now I see that's not the case, and why, and it makes sense.
It's too dark out now to go see which kind of tires I have, and it's not on the receipt I have for today's work (patching a puncture from a screw and checking the tread wear). This was covered under my service agreement, so it was free and maybe they didn't feel the need to put in details? (Why they have every detail in there about the car and nothing about the tires, when it's the tires that the agreement covers I don't know.)
Anyway, I believe they're Michelin tires. I know they're directional and top of their line, because I bought the best in order to have stability in rain and snow (but more in rain). I totally agree with you, the_same_mountainbike, about it being worth investing in them for safety.
What I really was looking for was how much longer my tires have? Andrew J, your answer really helped with this. I gather I need to replace them before 2/32. It's not just about avoiding a blowout, it's that I wouldn't want to drive with them once they can't hold steady in rain and snow.
Oh well, here's hoping I get a job well before the tires go and the car dies. It's 10 years old, has already had $1500 in engine and other repairs this year, has another $1000+ of repairs needed (engine mount, rear trailing arm brushes and then the brakes will be due for replacing soon and the transmission fluid, and the compressor needs replacing, too) and all this is even before the routine maintenance check, which I can't really afford...