Learn French: Quelle est la différence entre cette catégorie et l'autre ? - What is the difference between this category and the other?

We use entre (between) because we are comparing two distinct, explicitly named items: cette catégorie and l'autre. You use parmi (among) when something is mixed into a larger, undivided collective group, such as parmi ces catégories (among these categories).

Why do we start with Quelle est rather than Qu'est-ce que to ask 'What is'?

When asking 'What is [noun]?' to identify a specific fact, choice, or detail, you must use the interrogative adjective Quel/Quelle followed by the verb être. You would only use Qu'est-ce que if you were asking for the broad dictionary definition of the concept itself.

Why does autre have an article (l') in front of it?

In French, autre rarely stands entirely alone; it needs a determiner. Here, l'autre acts as a pronoun replacing the implied noun phrase l'autre catégorie. You need the definite article l' to specifically mean 'the other one'.

I sometimes see a similar word spelled différend with a 'd' at the end. Can I use that here?