How is a denatured protein different from a normal protein?

First of all, a protein consists of chains of amino acids and a single amino acid is coded by one codon of DNA. Mutations are able to insert, delete, replace and shift codons, which can result in amino acids being changed, removed or added, which would affect the protein that the amino acids are building.

For example;

Here is a strand of DNA in which the three codons in the middle codes for the amino acids.

....TGG ATT ATG GAG TTC....-----> Isoleucine, Methionine, Glutamic acid
Say that the strand of DNA has it's reading frame mutated (shifted).

....GGA TTA TGG AGT TC....-----> Leucine, Tryptophan, Serine

Notice how completely different amino acids arose from the mutation. Such a change may effect the protein's characteristics, as well as the phenotype of the organism.