Q:

How the attributes of god 'Rehman' and 'Raheem' different

Except surah 'tauba' all surah of Qur'an starts with "bismillah ar rehman ir Raheem".
How being rehmaan and being Raheem different?
An aalim explained that Allah is rehmaan for all the creatures. It does not matter if they believe in god or not, it does not matter they are good or bad.
And Allah is Raheem for some selected people.

A:

"Rahman" means merciful for all (believer or non-believer). Like sending rain, food,...
"Rahim" means merciful for believers only. 
Allah has two kind of mercy. One is for all. And one type is extra only for believers (Mumenin).
Source

A:

Some aalims (scholars) say: "Rahman" is a name ("Esm") not attribute, just for god. But "Rahim" is an attribute which used for passenger "Mohammad (ص)" in surah "tauba".
Two reasons are explained:

We can replace "Allah" instead of "Rahman" everywhere in the Quran.
"Rahim" used just in kindness of him, but "Rahman" used everywhere.

From here.

