AKA,
In most cases, Boeing procedure for the 737 is for either the Autopilot and Autothrottle to be both engaged, or both disengaged.
A couple of times that this is not the case are: after takeoff but before the Autopilot is engaged; if the Autothrottle is U/S; or when flying on one engine.
During an Autoland, the Autopilot will start to flare at 50' Rad Alt and the Autothrottle will retard the Thrust Levers to idle at 27' Rad Alt.
During a manual landing, both the Autopilot and Autothrottle will be disengaged, and so all inputs are entirely manual.
However, some pilots choose to 'deselect speed' on the Autothrottle for a manual landing. This leaves the Autothrottle engaged but with no mode selected (The Autothrottle is 'Armed'). Thrust lever inputs are manual but if the speed gets too low, minimum speed protections will kick in and nudge the thrust levers up automatically. This is not recommended by Boeing.
Regards,
PA28pilot