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Suppose there are two FA's F1 and F2  and given that  L(F1) = L(F2) then it means F1 and F2 are same .
Not necessary same, but similar. There can be different FA accepting same regular language. However, there is only one uniuqe minimised DFA accepting a regular language. Thus, if $L_1$ and $L_2$ are minimised DFA of same regular language, then they are certainly same (exactly).

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