Type of battle system.

You know when you can attack the monster and be attacked without
going into a battle mode?
I think it involves common events, switches and condition branches
but I still need a bit of help on this. Could anyone tell me some
games that have it so I could look. Or maybe give me a short
tutorial?

It's called ABS, Action Battle System. You can try to find a script somewhere (there are even a few on this forum) if you are using RMXP. It's rather hard to make with bare events and it also lags a lot that way.

links kai to blizz's own abs...

http://rmrk.net/index.php/topic,9533.0.html

rep++