Equivalent formulae with different CNF
It depends on the algorithm for obtaining CNF of a formula.
A simple truth table-based method will always produce syntactically the same CNFs for equivalent formulas, since it in a sense just gives you the rows of the truth table for which the formula evaluates to false.

A trivial example of equivalent formulas, which are both in CNF:

$$A \wedge B$$
$$(A \vee B) \wedge (A \vee \neg B) \wedge (\neg A \vee B).$$

Non-uniqueness of CNF means that one can build an algorithm, which returns essentially different CNFs for equivalent formulas. For example, as a first step the conversion algorithm can check if a formula already in CNF and return it immediately.