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?
Each battle that you win will yield experience for each pet that participated. However, deceased companions will not receive any experience (so make an effort to keep them alive by swaping in a different pet). Experience gains are based on your pet's level compared to the wild pet. Defeating a higher level opponent will grant more experience than a much lower level one, but be ready for a tough fight!