Intuitively you would think that the tide is being formed because the Moon is "lifting up" the water at the point closest to the Moon. But this contribution is actually very miniscule to the tidal effect. Instead the bulk of the tides are produced about 45 degrees away where the tidal force is parallel to the Earth's surface. This has the effect of dragging the water closer to the tidal bulge.
the water of an incoming tide doesn't feel "i'm being dragged uphill", it feels "hey, the earth is moving underneath me". it's all in freefall all the time.
you don't feel like you are rotating at 1000 mph (1600 kph) but you do feel your weight against the surface of the earth. same with the water, except it feels itself being squeezed by everything around it like you only feel that in the entrance to a crowded venue.
so, the water on the side toward the moon and the water on the side away from the moon would mostly perceive the earth as dropping away or coming closer (if they could perceive anything at all) where they are is always their point of reference