I am confused in the difference between one to one function and one to one correspondence. Please help me out to distinguish between the two. 
Thanks
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I would say (hand waveingly) a one to one function is a mapping from A to B that puts A & B into one-to-one correspondence with each other, for one to one and function as defined in your previous questions.
1. one to one means injective (a mapping $f$ which maps distinct
elements of its domain to distinct elements of its codomain, i.e. $f(x) \neq f(y)$
whenever $x \neq y$ )
2. one to one correspondence means bijective (a mapping $f$ which is injective AND for every element $y$ in the codomain of $f$, there exists an element of $x$ in the domain of $f$ such that $f(x) = y$ )