Hybrid vs High Demand on a heat-pump water heater
Hybrid aims to use the heat pump as much as it can. High Demand, where a model has it, uses the electric elements more, so the heater recovers faster when you need more hot water.
The difference, line by line
What it's for
Hybrid: Matching a standard electric water heater's hot water output while using the heat pump as much as it can.
High Demand: Higher than average use, such as when you host guests from out of town.
How it heats
Hybrid: A mix of the efficient heat pump and the electric resistance elements.
High Demand: The electric resistance elements are used more, so the heater can recover more quickly.
Energy
Hybrid: The aim is to keep the electric elements' use low.
High Demand: More energy is used to meet the higher demand for hot water.
What DOE says each mode does
Hybrid
A combination of the efficient heat pump and electric resistance modes. The general idea: use the heat pump as much as possible and the electric element as little as possible, while matching the hot water output of a standard electric water heater.
High Demand
For higher than average use, the electric resistance elements run more so the heater can recover more quickly. More energy is used to meet the higher demand. Not all products have this mode.
What this doesn't tell you
Which setting to use on your model, how long recovery takes, how much energy each mode uses for the same load, or what it costs. Hybrid's aim is not a promise of output. For your heater's modes and its default setting, check the instructions for your exact make and model.
Source
The mode descriptions come from DOE's guide to buying efficient residential water heaters.