Autocannons are not machine guns
Usage is just an example of how the word is sometimes used. A definition is what the word actually means.
Are you pulling my leg?
One definition of "car" could be "a vehicle used for transportation" while usage could be "Jane drove the car to the store."
Of course, but when you say that sentence, you're using the word "car" and intend it to mean something specific. That's its definition; it's what people mean when they say it.
In this case, when people say "cannon", they sometimes mean something that could also be described by the word "autocannon". So in that sense they are synonyms. Therefore, one of the definitions of "cannon" is "autocannon".
If you want to say that one of the definitions of "autocannon" is a "cannon" with certain particular characteristics, then I'm ok with that. I'm not ok with saying that a "cannon" is an "autocannon" because that would be a lie.
I've decided I can live with adding "sometimes used as shorthand for "autocannon", when mounted on aircraft" if it's genuinely important to you. Emphasis placed on shorthand.
But CodeCat's examples are unlike either of yours- I think you're reanalyzing things without realizing it. A definition is just a tool for presenting a meaning- it doesn't determine meaning, unless it's adopted by users of the language. As for the meanings themselves, they can't exist independently of usage. Any language is a negotiation between those who use it: everyone may have a different idea of what a term means, but only those meanings that are understood by the one producing and the one receiving will work: I may be convinced that German means extraterrestrials with three ears, but if I use it that way, no one will understand me, and if I try to assign that meaning to what others say, I won't understand them. The way this negotiation works is through usage. At one time, an earlier form of hound was a general term for any dog, but at some point, it became restricted to a particular type of dog, and the earlier form of dog became the general term. The kind of things CodeCat is talking about are hidden parts of the meaning that may, at some point, become explicit and thus part of what you would call the definition. Even now, people tend to use qualifiers for any type of milk that's not from a cow: goat's milk, mother's milk, etc. That's a sign that things are already heading in that direction.
Chuck, you wouldn't list "short for goat's milk" as a definition for the word "milk". You could, on the other hand, list "milk that comes from a goat" as a definition for "goat's milk". So, you could go to "desktop personal computer" (if it was one word) and add a definition that it's a certain type of computer, but you wouldn't list desktop personal computer as a definition of computer.