No dumb questions on here!
NOAA, as well as USPHS, wear Navy-style uniforms. There are 5 armed services, 7 uniformed services. NOAA and USPHS are not armed but uniformed. Each of them has a commissioned officer corps.
Not sure how USMMA manages who wears what at graduation. I've met lots of NOAA-folk out of USMMA. It's a fine way to go. NOAA does some interesting stuff and has privileges at military bases, etc.
One sure thing... this has been going on so long, there's plenty of history, plenty of briefings along the way when it's time to indicate interest in certain paths.
And if you ever see a full-bearded guy who looks like a naval officer, it's probably Public Health!