Can a language be the one recognized by more than one automatons?
Yes, of course, it is possible.  For instance, the process of DFA minimization works as follows: given a DFA $M$, produce another DFA $M'$ that recognizes the same language but is as small as possible.  That tells you that it is possible to have two DFAs (deterministic finite-state automata) that recognize the same language.

If you want an explicit example: Let $M_1$ be a DFA with a single state (which is accepting) and self-loops on inputs $0$ and $1$.  Let $M_2$ be a DFA with two states (which are both accepting) and edges from state $s_0$ to $s_1$ on inputs $0$ and $1$, and edges from state $s_1$ to $s_0$ on inputs $0$ and $1$.  They both recognize the language $\{0,1\}^*$, i.e., they are two different DFA that recognize the same language.

The same holds for other common families of languages, e.g., context-free languages and pushdown automata; context-sensitive languages and context-sensitive grammars.