If we look at a tiny fraction of DNA, I may be able to show you what I mean.
Say that the code for a bird's digestive tract structure begins with these two codons (triplets of nucleotide bases that represent an amino acid in the protein chain) is as follows:
ACG TAC AAG
Now, say a mammal's digestive tract is coded like this:
TGG ACC TCG
If you look, you'll see that each case uses the SAME nucleotide bases to code for proteins. A=adenine, T=thymine, C=cytosine, G=guanine.
However, the ORDER is different, meaning the protein will be different. That means that the structure and function will be different in the two different species.
See? A is tricky; you need to understand that it's not saying the code is the same, it's only saying that all organisms use the same 4 nucleotide bases to code for proteins, or the same genetic alphabet. We use 26 letters in English to spell millions of words, by putting the letters in different orders. In genetics, 4 'letters' are used to code for millions of different proteins depending on the order in which they are arranged.
Another way to see this is that most locks use tumblers, but only one key will fit a particular tumbler. You can't use your car key to open your front door, for example. The order of nucleotide bases is different in a bird than it is in a mammal in the same way. While the bases used are the same, they are in a different order in each species.
I hope this helped to clear this up for you!