Yes there is Difference in them ..
Have a look at 1st (a+b)* means ...we can have "aaabbbaaa" or "aba" that is after b we can have a again in 1st language..
but when it comes to 2nd language ... a*b* = here once b has occured there is no way we can have occurance of a .. so "aabbaa" is not allowed in 2nd language ...
(a+b)*=(a*b*)* but a*b* is not equal to (a*b*)*