There is no actual distinction between the Aesir and Jotun. They're all Jotun essentially. The reason the Aesir, such as Thor, kills so many Jotun is to protect Midgard from them who wish to destroy humans. This, in many ways, can be seen in Greek Mythology between the Olympians and the Titans.
Yeah I noticed the parallel.
Do you know why both those cultures have a similar concept? Are there other mythological concepts that do the same thing?
Chances are that it's due to meshing of cultures, along with travelers and merchants who may have introduced various cultures to different people. Can't be sure, though.
I think Sumerian mythology shares this concept as well.