Analogy: think back on riding the swings in kindergarten. Was it fun? Now, imagine going back to those swings exactly as they were, and sitting in them now, as an adult. They're too small. They don't fit. Your feet drag on the ground because they're so low to the ground. The bar over your head is low enough that you can reach out and touch it, and even at the highest the swing will go, it's only about chest high when you're standing up. It's exactly the same swing, but riding on it now is a very different experience, yes?
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Blizzard said it will choose players who have active subscriptions to the regular game based on a variety of factors to help them test the beta. It could be based on your PC, your commitment to the game, or just your luck. If you get in, you’ll likely receive an email, but if not, you can check your launcher. And remember: as with any beta, your progress will not be saved for when the game launches later this year.
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.
If your pet's health gets too low or its attacks aren't very effective against a certain combatant, you can always switch out your current pet with another companion on your team. Only pets that are considered active (i.e., those in your three Battle Pet Slots), may be switched in and out during the battle. Once the match is over, you can always change up your active pet team, which is useful if one of your pets is low on health or dead.