Only really to expand on Gráinne's comment as regards the 'collecting' and 'roster development' sections - which are, as said 'distinct' although they are intrinsically linked - I would like to point you in the direction of the in-game Achievements > Battle Pets > Collect tab. There are a series of achievements called Raiding With Leashes, pretty much all of which can be completed via the auction house - if you have the gold/inclination - or by completing old raids.
Each pet has 3 abilities it can use during a battle, but a total of 6 to choose from. They will also have a total of 3 active spell slots that show which abilities can be used during a Pet Battle. The first spell slot will already be unlocked, but the second and third will only become available once the companion has reached a certain level. Other spells will also unlock after reaching higher levels.
Learned this today: posted a comment, came back later to see if there was any feedback, reloaded the page: the page posted a copy of my comment. That was not what I wanted. I just wanted to check if my comment was posted and if there were some responses. I did not want to post a copy of my comment from 5 hours ago. And, a humble guess, I think the majority of the users are not expecting such behavior either.