Nurse
But it's not the same, is it? The ship or sqadron doesn't have the same long term staff postings, at least as I understand things. The regiments, however, are an individual's focal point: whilst people will have postings away, they return to the regiment regularly and keep the affiliation even after being promoted out of the regiment if they get to that rank. (Col/Brig xxx, late the zzz regiment).
In the RN and RAF, again, as I understand it, an individual will have a number of postings to different ships/ squadrons/staff postings without the central focus provided by a regiment.
Happy to be corrected if my thinking is mistaken.