Besides increasing pets level, does training raise their stats like exploring?

Yes, it works exactly the same.

When your pet increases its level, it increases the stats according to how you've been feeding it. Otherwise, what would be the point of leveling? The differences between the two methods are listed below:

Training can be done even if your pet has zero energy; it needs at least five energy to explore.

Training costs silver depending on how much XP is needed; exploration is free.

Training will get you exactly enough XP to level; exploration might get you a few points over, or a few points under.

Training gets you to the next level every time, and does nothing else; exploration may or may not level you, but you also find stuff like money, food, and materials.

Training does nothing to help research your pet's genes; exploration can end you up on islands with free verillium and even buildings that research random genes for free.

Training takes several hours to level in a single session; exploration takes a few minutes each session for two to twenty sessions, depending on how much XP is needed.

All in all, I'd explore as much as you can each level, and then use training to top it off.

Thanks to you both! :)

And you also get matirials from the exploring I dont supose the training to do that to (I am new so I am not sure)

I like battling my pets, then training, or exploring then training. Since they don't need energy to train. I feel like I get the most out of my pets like that.