I don't know why I didn't think of this first. Anyway, it was good advice, and I tried it. I've checked out the Sunrace site and the Shimano site, and it looks to me as if several things are true:

1.) Within a given company, sometimes the difference between product lines is purpose, not quality. Derailleurs are designed for certain kinds of cassettes with certain numbers of teeth (I didn't realize this), so if you want, say, an 11-34T cassette, you can only use certain kinds of rear derailleurs, whereas a different cassette might allow/require a different kind of rear derailleur. These different kinds of derailleurs have different prices because they're different, not necessarily because one is better than another.

2.) Sometimes the higher-grade product lines are different in such minor ways (say, Tiagra vs. Sora) that a non-professional cyclist like me will never be able to discern any difference at all.

3.) The bike salesman who told me that the more expensive bike would have more precise shifting because it had more expensive components was probably mistaken and possibly lying. (I'll give him the benefit of the doubt and assume that he was just repeating what he'd heard everyone else say.)

Is this a fair assessment? I'm a newbie, so I'm still trying to sort all this out. Thanks for the insights.