Enlisted only have rates, not ranks. It’s a weird navy thing. Enlisted also have “ratings” which is your job, I.e aviation tech, boatswan, etc.
Youre also talking about firemen/seamen/constructionmen/etc. These roles are e-1 to e-3 and have a rate, but not a rating.
In my experience, no one knows the rank/rate distinction and everyone just refers to rank. It’s not something they explain well.
Youre mistaken. A “rate” is where you are on the E1 - E9 paygrade scale. A “rating” is your assigned job, what you get after A school. A Fireman has a rate of E-1/3. He does not have a rating because he hasn’t been to A school. You can also “strike” for a rating by testing into it, but thats rarer.
There is more history about this confusing system here Note that this is from a .mil site specifically about Navy history. The article is from 2019.