Hi,
Savage As an adjective, this means 'fierce, cruel'. A savage lion. A savage robber. A savage attack.
It can also be a noun.
Wild Has more meanings. Some examples of 'wild' that you might want to compare to 'savage' are:
uncivilized, undomesticated = a wild lion (not a tame one)
in the natural state= a wild flower
Best wishes, Clive