They are just variants, they mean the same thing. I think "sálja" may actually be the "correct" version.
It somehow depends on the letters of the word whether it gets a "-ja"/"-je" or just an "-a"/"-e". The word "sál" may be a borderline case.
Láb-a, hát-a, váll-a, kabát-ja, kalap-ja, sál-(j)a, bál-ja ("bála" is a different word), tál-(j?)a, pár-ja ("pára" is a different word), vár-a ("várja" is a different word), asztal-a, fiók-ja ("fióka" is a different word), talp-a, etc.
And then there is sár-sara, kanál-kanala, pohár-pohara, szél-széle, another szél-szele, etc.
And it gets worse before you learn it all. Enter the "assimilation". :)
Ok I can accept that this is the "third person plural" but maybe:- "their car, or their house" but their scarf! really? are we to assume that THEY a couple perhaps are sharing the scarf? he has it in the morning and she in the afternoon! Couldn't Duolingo chuck in a few ónónő's to try and confuse us a little more!
Sure, no problem, let it be "az óvónők sálja". :)
The point is, even when it is each their own, Hungarian can and usually will say it with singular.
"Ebben a városban a nők sálat viselnek."
This is, literally: "The women in this town wear scarf."
Not "scarves", and not "a scarf". Just "scarf".
My best advice is, think of it as an uncountable object. If it were "fish" or "flour" or "bread" or "sheep", you would have no problem with it being singular, would you? The best way is to treat everything like that. Or almost everything. There is no grammatical difference in Hungarian between everyone sharing a single thing or everyone having his/her own.