difference matane and jaane?

As far as I know both mean see you later in English and in more ore less informal context. But are they different in the Level of politness ?

I don't think they have different levels in politeness. I haven't hear of that once.
"Mata" means later and "ne" means ok? or something like that "Mata ne" as you said see you later.
"Jaa" means then well and "Ne" as I told you Ok? which means see you later as you know.
That's what I know but my level is lower intermidiate therefore I prefer you wait the other answers!

"Jaane(じゃあね)" is short of "Jaa, matane(じゃあ、またね)".
"Jaa," means just "Well,/OK!," using for friends same age or younger mainly.
More shorter "ja,(じゃ、)" also saying a lot.
No difference as meanings.

Formal style is "soredewa, mata(それでは、また)"or shorter "dewa, mata(では、 また)".
Jaa,(じゃあ、) is one of casual/friendly word of "Conjunction(接続詞 : setsuzoku-shi)".
http://ejje.weblio.jp/sentence/content/%E3%81%98%E3%82%83%E3%81%82%E3%...
http://pothos.main.jp/setuzokusi.htm
http://pothos.main.jp/html/140428a.htm

However, in out of Tokyo and around, it is common to use their dialects(方言/hougen : local words).
Shittake(ne)!/したっけ(ね)! in Hokkaido (mainly Sappo and around),
Heba(na)!/へば(な)! in Aomori,
Hona(ne)! /ほな(ね)! in Osaka and around, and some more are very famous.

"Jaane(じゃあね)" is short of "Jaa, matane(じゃあ、またね)"

I doubt that most Japanese think of it that way. "Jaa" means "well then" and you can use it in combination with a lot of words. It doesn't necessarily imply "mata".

I would say that "matane" is like "See ya." and "jaane" is like "Okay then." But as it is in English, you might say "See ya" and know that might never see each other again. Both are simple and casual ways to express "Bye."