After a few weeks of repetition, I can answer my own question.
रही/रहा /रहे are used for the present continuous (progressive) tense . "is *ing " चल रही है means "is walking (female(s))"
चलती means "walks"; this is the simple present tense.
Extra credit: There is also a "present perfect progressive" tense, in English "has been walking". I don't know whether the Hindi present perfect continuous (progressive) is covered in this Duolingo learning tree, but I found a few other lessons online (1) (2). If I understand correctly, "Grandmother has been walking" is "दादी चलती रही हैं"
Well, rather less confused after that great detailed post by ErikaKretz (that Lingot is from me, by the way - many thanks!). It looks like the main difference between present continuous and perfect continuous is that the verb has some sort of suffix to indicate past tense.