Yes, this is a deep subject and "Genetics" is indeed the correct term. Our company is called "Genomics" because of the origins of the founders in the Oxford stats department and Big Data Institute.
Both Gil and Peter have done some incredible things in this space, but the language of scientists can be difficult to understand by a lay audience.
There are a lot of caveats in representing a genome as some point diffs from a reference. I worry that your description might promote a way of thinking about genomes that ignores the more complex things that can and do happen.
You may (at your own risk) take a look at
https://opensnp.org/