They are synonyms. אך is rather archaic, you wouldn't hear it in daily conversation, but it would sometimes appear in written language.
What about אלא ? Is אבל more like however/although, while אלא is more like rather/instead?
The word אלא is used for a different meaning of but. I think it's not very common in English nowadays.
When the second part is complementing the first part use אלא
It was not me, but him - זה לא היה אני אלא הוא
When but adds a certain contrast, it's אבל
I ate it but I didn't like it - אכלתי את זה אבל לא אהבתי את זה
Agree? Or ate?
And what about ".אני לא אוכל בשר, אלא גבינה" ? Seems like the second part contrasts with the first...
I think the English sentence should have a comma, like so: "He hates me, but I do not hate him." Hebrew doesn't seem to use as many commas as English. Is that true? Or are the Duolingo sentences just a little more lax on grammar?
I've read the same thing. They don't use as many punctuation marks and many are from Western language.