The analysis is correct: capital B for the Bitcoin network, which is the interesting part, and small b for the token
Sorry but you seemed to forget that bitcoin is bitcoin, a coin with its own native blockchain and it is not a token. I believe you did knew about it, just made a mistake in the post when typing.
Newbies can read
Definition of tokens. and learn about token definition.
It's just usually that we use the word token when we send something from one place to another place, but you are right.