I finally figured it out

I've never really known what the difference was between Hispanic and Latino.  Given how sensitive racial sensibilities are in the modern world, I felt bad going around using one term if the other one was really appropriate.  For some strange reason, I don't have any friends who are Latino or Hispanic so I wasn't able to ask (and I never felt comfortable walking up to a stranger to ask).  That's where good ol' Wikipedia comes to the rescue:

Hispanic - Wikipedia, the free encyclopedia

Turns out, in order to use the correct term, you (a) have to know where the person was born and (b) know what their ancestry was.  If someone was born in Mexico, or another Latin America country, but their ancestry was completely indigenous with no Spanish bloodline, then they are Latino, but not Hispanic.  If they were born in Brazil or another formerly Portugese colony, then they are not Hispanic.  But if they weren't born in Latin America, then they aren't Latino.

Bottom line: it's a safer bet to use the term "Latino," and it seems to be the term that people from Latin America prefer, partially because it emphasizes their own geographical region, and not the country that used to colonize them, and also partially because it is seen more as a self-chosen term, instead of a term that was applied by an outside colonial power.  (It looks like the term "Hispanic" only came into prominence in the 1980 US Census, when it was an option for ethnicity.)