Both are phrases often used after mentioning any Islamic personality who came after the sahaaba (radiallaahu ta'aalaa 'anhum ajma'een).
Rahimahullah means: Allah have mercy upon him.
Rehmatullah alaih means: May the Mercy of Allah be upon him.
So they both mean the same thing. From personal observation, rahimahullah tends to be used more in the Arab world, whereas rehmatullah alaih tends to be used in the Indian subcontinent. Other than that there's no difference. It doesn't really matter which phrase you choose.
ok and whats the difference in salawatullahi wassalamu alai
usually when we take prophets name we say sallallahualaiwasssalam
but i heard imam awlaki saying that so whats the difference and meaning of that?