OK, let me just break this down for you. Rates are a job in the Navy. For example, in that wikipedia article, a Fireman recruit is a rate – their job. Their rank would be a Seaman Recruit. Their paygrade would be an E-1.
In your example, a Constructionman would be an E-3. Constructionman would be their rate. Their rank would be Seaman.
You can see this better at https://www.defense.gov/Resources/Insignia/
They don’t list rates, because there’s many, many, many different jobs in the different branches. The Navy is odd in that they usually refer to each other by rates, not ranks. In every other branch, people usually refer to each other by rank and not their MOS/AFSC/Whatever. It would be weird in the USAF for example to refer to some Airman First Class as 2A33C or whatever.
You can see this further explained at https://www.military.com/navy/enlisted-rates.html where they list the rates and talk about them but then they list the ranks and talk about them. They are tied together by paygrade.
And once again, in the US Navy, an enlisted person can literally not have a rate and be called Unrated until they are assigned a rate. Usually this happens to very junior enlisted.
I don’t want to keep replying to this but in response to your ‘this is from a .mil site specifically …’ I linked to the DOD’s actual gov website.
This article is relevant for NAVPERS 18068F because the Navy has all of this annoying traditions, like referring to ‘-’ as Tack like they are pretending to be a flagman from 1835 on a ship and refer to a snackbar as a gedunk and blah blah blah.
But they still have a military rank. Sure, if you ask someone enlisted person what their ‘rate’ is they are going to respond with “PO1” if they are a Petty Officer First Class but if you have a CAC ID, under RANK it is going to say PO1 with the USN’s seal in the top-right. Because it is their military rank. The USN can call it a rate as well and traditionally it can be known as a rate in the USN but it is still a military rank. It will even say that on your ID card if you have one or have had one. As I recall, this is also true for the old green ID cards.