Language acceptance by DFA
Yes, there can be many DFAs for a language. Many will be silly though, one way to get another is to add unreachable states to any DFA for the language). It is also possible to have more than one sensible DFA:



These two DFAs both accept $\{a,b\}^{\ast}$.
On the other hand each DFA accepts exactly one language (i.e. no DFA accepts zero languages, or two or more languages) .