Sort of but not exactly. The way I'd explain it as someone who's had to deal with a lot but has not been formally trained in it is that WGS 84 is a system for reasoning about the earth spatially. EPSG:4978 and its more commonly used sister EPSG:4326 are standardized ways of writing down coordinates relative to the WGS84 model of the earth.

The "joke" in my comment is that EPSG:4978 coordinates are written down in distance in meters from the center of the earth, as a sort of absolute position that's nice to use in maths. In contrast to EPSG:4326 where coordinates are written down (usually in degrees) relative to the equator and a line through some place in England over an idealized representation of the surface of the earth.