Does an external startup disc work like the internal hard drive on a M2 Mac Mini

Generally speaking, yes, an external drive does work like the internal drive.

The internal drive in an Apple Silicon Mac (M1, M2) is an on-chip design, built into the cpu, and works as an SSD.

An external SSD is very similar. An external platter drive or hdd is mechanical in nature and slower.

Your external drive may be used for data storage and/or as a startup drive for your Mac.