is a grease seal the same as an oil seal?

As Gordon said the terms have lost meaning. Here is the old convention in the context of rotating shafts.

A grease seal is meant to hold back grease and would normally be low speed. This means no need for or possibility of a hydrodynamic seal. Not much consideration for wear either.

An oil seal is designed to hold back oil, must develop a hydrodynamic sealing surface and also compensate for runout and wear. To do this oil seals are more flexible and have a defined sealing lip that is spring loaded. Some have nternal features near the lip to push oil away from the lip to aid sealing but make them unidirectional.

So the convention may be lost but it shouldn’t be. There is a difference in design and function. Something like all bushings are bearings, but not all bearings are bushings.