Yes, there is a difference between a wave of zero amplitude and completely still water.
A wave is a disturbance that propagates through a medium, such as water. It carries energy from one location to another without transporting matter. Waves have characteristics such as amplitude, wavelength, and frequency.
Amplitude refers to the maximum displacement of particles from their equilibrium position as the wave passes through them. In the case of a wave with zero amplitude, it means that the particles of the medium, in this case, water, do not move from their equilibrium position at all. The wave still exists conceptually, but it does not cause any physical displacement of the water particles.
Completely still water, on the other hand, implies the absence of any wave or disturbance propagating through it. The water molecules are in a state of equilibrium and remain stationary. There is no energy transfer or propagation of disturbances in completely still water.
In summary, a wave with zero amplitude represents a wave that exists but does not cause any physical displacement of the medium's particles, while completely still water implies the absence of any wave or disturbance propagating through the water.