Is it possible for 2 different DNA sequences to code for the same amino acid?

Potentially, yes.

A single amino acid can have multiple codons. For example, both the codons UAU and UAC code for tyrosine. Francis Crick first described this as "wobble."

So you can see that two genes with slightly different bases can code for the same sequence of amino acids. If both genes are identical except for one changed base pair, the chances that the resulting polypeptide will be the same for both isn't particularly high, but there is still a chance. The chances decrease with every base pair substitution.

This has implications in mutations, as a point mutation may or may not change the protein in translation. If it doesn't due to wobble, the mutation is said to be "silent."