As an Italian, I really don't know the logic behind the number. I also asked my mother, to no avail. We don't know, but as far as my feeling goes, it's just a numbering system for the product, e.g. there's no implicit meaning into it.
As far as we worry about it or not, sure we do. Matching the wrong pasta with a given sauce is almost blasphemy and as a feedback for the mistake you can be frowned upon up to being openly insulted. I'm not kidding. For example, meaty stuff (such as ragu', also known as bolognese, but only outside of Italy) are matched with penne, tagliatelle, fusilli, and in general all egg-based pasta (e.g. strozzapreti, paglierini, pappardelle, spaghetti alla chitarra). Spaghetti bolognese is heresy for us.
Spicy sauces, such as puttanesca, amatriciana, carbonara and so on, require normal pasta, and can be matched with spaghetti, or also penne. Pesto always goes with bavette, although sometimes we use spaghetti for convenience, but I feel it unnatural.
To sum up, there is no simple rule, although instinctively, if you tell me a sauce (even invented brand new) I can tell you which pasta is appropriate and which one is not.