Why is equivalence in logic said to work similar as a XOR gate? An if `equivalence` is shown in logical statement, it means that it both the statements are logically same but we refer to it as `XOR` gate(which is 1 when the inputs are different). Shouldn't it be `XNOR` gate representing equivalence?

Well, an XOR gate with inputs $A$ and $B$ can be described by the table:

$$ \begin{array}{ c | c || c | } A & B & A \textrm{ XOR } B \\\ \hline 0 & 0 & 0 \\\ 0 & 1 & 1 \\\ 1 & 0 & 1 \\\ 1 & 1 & 0 \end{array} $$

whilst $A \Leftrightarrow B$ has truth table: $$ \begin{array}{ c | c || c | } A & B & A \Leftrightarrow B \\\ \hline F & F & T \\\ F & T & F \\\ T & F & F \\\ T & T & T \end{array} $$

If you interpret 0 as "false" and 1 as "true", then, yes, an inverted XOR gate would be more appropriate. But if you interpret 0 as "true" and 1 as "false", then a regular XOR gate will do.