I want to know who told you that DNA carries genes like I would carry an apple rather than genes literally being a part of the DNA, so that I may slap them.
But for your sake, here's what a gene is: "A gene is a sequence of DNA or RNA which codes for a molecule that has a function." The "or RNA" applies to the few viruses that use RNA as their genetic material instead of DNA. Regardless, genes are a part of the DNA sequence directly, not something merely chemically attached to it.
HOX genes are the most highly conserved genes among all animals. Humans have some HOX genes which are entirely identical to those in fruit flies, the organism used to find these genes to begin with. Heck, by virtue of DNA having only 4 different bases, equal sized genomes of hypothetical organisms entirely unrelated to each other will have their bases match up 25% of the time just by chance.
I sincerely hope that you do not think EVERY gene has to be different between individuals for them to have different physical traits. Heck, technically, genes could be entirely identical between individuals and they can still end up with minor differences, which is why identical twins often grow up to not look entirely the same, despite having identical genomes. After all, the environment plays a role.
No harm done, misunderstandings happen.
If you are going to use the term "kind", please define it, because there is no standard definition of what "kind" actually means. Some people use it to mean species, others genus, etc. However, evolution doesn't claim that a chicken can hatch from a lizard egg or other such nonsense. Rather, that minor differences in populations created by mutation can change in frequency within that population, and over time this process can lead to major changes over many generations.
Then how does a frog start out as a tadpole? Also, I would think that the fins of whales would count as aquatic characteristics.