What's the difference a Detachment NCOIC and a Detachment Sergeant?

Having done this job, they're pretty much the same thing. The main difference lies in where the command authority lies. If the detachment OIC has it, you're the detachment Sergeant. If it resides with a Company Commander, you're the NCOIC.

SFC (Join to see) great question, from my experience: Detachment Sergeant is like the 1SG in duties and scope of a Company (HQs) and Detachment NCOIC is like the S3 NCOIC in charge of a section or teams.

This is the third HHD (Headquarters and Headquarters Detachment) that I've been assigned to in my career. The Detachment Sergeant is equivalent to and performs the same job as a 1SG but doesn't have the rank and runs a much smaller unit than a company. An HHD is a permanent headquarters unit and has an MTOE or TDA.
The name Detachment NCOIC implies that the Detachment is a temporary detachment from a regular unit. This is my experience.

They can call the position anything, but look to a few places. The TDA for the authorization, and the title and lawful power of the officer you support. Both reflect the unit structure and what your position really means.

This would be my take on the subject. The Det NCOIC would be a temporary job and a Det SGT would be the NCO in charge of the Detachment HQ. Liken it to a mini-company HQ. Back when, the BN had HQ company and the higher ups have a Detachment HQ. Confused yet?

NCOIC - Non Commissioner Officer in charge, Detachment Sergeant could be a detachment under them or on another base. No sure if that's clear!

It all depends on the job position as specified in the unit's TDA.

Detachment NCOIC is incharge and Detachment Sergeant is not

Could be the Line and Paragraph Number. Could just be a difference of the official title.