"Shape" is not even "context," much less "data."
To differentiate between the DNA of various life forms, we examine the sequential data stored by the bases in each DNA strand. Neither the "shape" nor the "context" can tell us which life form is coded in any particular DNA, but the data can tell us that answer.
Correct. Shape is affected by context and is important for FUNCTION.
To differentiate between the DNA of various life forms, we examine the sequential data ...
Naturally. And to compare compare dentition between fossils we examine features of teeth.
There are many ways to compare different organisms. We happen to be able to manipulate DNA sequence pretty well. It's the easiest place to start. Unlike software programs, however, given DNA sequence we still can't predict function. Sure, some of the sequences have been figured out: ie this type of sequence gives the following structure, like an alpha-helix. From there, we still don't know what it does.