In computer graphics, wireframe means literally just a frame of lines(wires), meant to represent some other 3D shape(such as a cube). What is the opposite of wireframe, as in colored in normally like a solid object?
The opposite of a wireframe object is, as you've already noted, a solid object.
One might also refer to a matcap or textured object - these would normally be understood as solid although in reality they might still show the wireframe drawn over the solid face.
Another alternative (in between solid and wireframe) is a transparent object. In 3D usage that implies partial transparency of some/all of the faces allowing you to see areas of the model that wouldn't necessarily be in view in solid mode.
Surfaces or solids. Wireframe uses only curves (2D or 3D) to indirectly model (represent, suggest, render) surfaces and solids.
Representations that display surfaces and solids are contrasted with wireframe models, but even such representations are sometimes just based on wireframe models (i.e., only curves are used to define or suggest the surfaces and solids). IOW, the representation is just rendering, with no underlying surfacic or solid mathematical model.
Mathematical representations of surfaces and solids are a better contrast with wireframe: the surfaces and solids are directly modeled by mathematical or algorithmic objects.