I do not know what type of "style" name you give this type of playing, i have called it "overlap guitar" as two guitarists play two differant rifs in two differant keys at the same time: Zacky and Synster gates from Avenged Sevenfold, do it in lots of there songs. An example of when it is played is in Beast And The Harlot when Gates plays the 1st solo, mid way through the solo Zacky and Gates play the "overlap guitar". On the album version i have (which idowloaded from itunes), the "overlap Guitar" starts at 2:09 and finnishes at 2:15.

My question is:
What is the technical term for this type of playing as i want to learn how it work so i can use it in some of my bands songs as i think it sounds fantastic?

Take a riff and transpose it, errr start it on the 3rd, 4th, 5th, 7th, etc.

And yes its just called a harmony.
Theyre not playing in a different key, just playing different notes in the same key that are in harmony

It's called harmonising
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I'd say harmonising from the description, but i haven't heard the solo.