What´s the difference between 世界(せかい)　and 世(よ) if both mean world?
Well, i wanna know when to use both words.
Also what´s the meaning of this word 転世.

Question

Answer

世界 means world and country.
e.g.　世界の国々(countries all over the world)
　　　　世界一周旅行をする (to travel all around the world)
        世界中の人々（people from all over the world）
        自分の世界に引きこもる（to retreat inside myself, to shut myself away from society）

世 means life, society and world
w.g.　世の終わり(end of the world)
　　　　死んであの世へ行く（to die and cross over to the other side）
        世に知られる（to be well known in the world）

I think　転生（てんせい・てんしょう） is correct, not 転世.
転生 is usually used as 輪廻転生（りんねてんせい・りんねてんしょう）, and it means transmigration.

Answer

My teacher once has told me the difference, sekai  世界 means world related to country to country, while yo 世 means life. In Japanese, there is a term 'kono yo' 'ano yo', kono yo means this present life and ano yo means the other life.