According to the definitions I have, the map in topology is continuous if the preimage of every open set is open. The map $f:X \to Y$ is called an identification map if it is continuous, surjective and also if the open sets of Y are exactly the subsets $A\subset Y$ with the property that $f^{-1}(A)\subset X$ is open in $X$.
I do not understand how the last condition of the identification map definition is different from the preimage of open sets being open in the definition of a continuous map. I get that an identification map must be surjective, which is different from a continuous map but it seems that there is more that I am missing.