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.