Unambiguous grammars with different right and left hand derivations
Consider the following simple grammar:
$$
S\to AB \\
A\to a \\
B\to b
$$
Here is a leftmost derivation of $ab$:
$$
S\to AB \to aB \to ab
$$
Here is a rightmost derivation of $ab$:
$$
S \to AB \to Ab \to ab
$$
You can see that they look different. However, they correspond to the same parse tree:

More generally, each leftmost derivation corresponds to a parse tree, and this correspondence is a bijection; and the same holds for rightmost derivations. Therefore each leftmost derivation has a corresponding rightmost derivation, sharing the same parse tree.