All three rest on the same foundation. The difference lies in how the channel is opened and how the graft is placed.
What they share: extraction
In all three, follicles are taken one by one from the donor area with micro-motor punches. So the "FUE or DHI" question is not about how the graft is harvested but how it is implanted.
Classic FUE
Channels are opened with steel slit blades and grafts are placed with forceps. Fast, and economical over large areas.
Sapphire FUE
The same flow, but the channel is opened with a sapphire blade. A sharper cut, a smaller channel, less oedema and the option of denser placement.
DHI
No separate channel step: the Choi implanter opens the channel and releases the graft in one motion. It is the best fit for unshaven work.
So which is better?
There is no single answer. Across a wide Norwood 5 pattern, Sapphire FUE moves more grafts in one session. If you are densifying between existing hair, DHI is clearly ahead. Your hair should choose the method, not the clinic.