Solid wood is a claim about some of the piece, never all of it

The term is not meaningless, but it covers far less of a piece of furniture than most people assume.

Why no good piece is solid wood throughout

Almost no piece of case furniture is solid wood throughout, and the good ones are not trying to be. Large flat panels made from solid timber move with humidity - they expand across the grain in a damp season and shrink in a dry one, and if they are constrained by a frame they split. This is not a manufacturing failure; it is what wood does. A wide solid tabletop has to be engineered specifically to allow that movement.

So the sensible construction for a big panel is a stable core with a real wood surface on it, and that has been true in fine furniture for centuries. Veneer over a stable substrate is a technique from the best cabinetmaking tradition, not a cost-saving imitation of it - it is the only way to get certain figured woods, like burl or crotch grain, onto a flat surface at all, because those cuts are far too unstable to use in solid form.

The terms, in the order you meet them

The terms, then, in the order they are usually met:

Solid wood - the named parts are timber all the way through. Read carefully: it commonly refers to the legs, frame and rails while the panels are something else, which is often the right way to build it.

Solid hardwood - as above but specifying a hardwood species. Oak, maple, cherry, walnut, ash, birch. Hardwood is a botanical classification, not a hardness rating, and some hardwoods are quite soft.

Wood veneer - a thin layer of real timber bonded to a core. Quality depends almost entirely on what the core is and how thick the veneer is. Over plywood it is excellent. Over particleboard it is adequate until the edge gets knocked or damp.

Engineered wood / manufactured wood - a broad category covering plywood, MDF and particleboard together. It permits a very wide quality range and is the phrase to ask a follow-up question about.

Laminate / melamine - a printed surface, not timber. Durable, wipeable, and it will never be anything else.

Check the edges and the inside

What to actually do with this: check the edges and the inside. Plywood shows its layers on any exposed edge and is a genuinely good material - stable, strong, and used throughout high-end joinery. Particleboard shows a uniform speckled crumb, is heavy, holds screws poorly, and swells irreversibly if it gets wet. Open a door or drawer and look at the unfinished internal edge, because that is the one nobody bothered to disguise.

The short version is that veneer over plywood beats solid wood over a bad frame, every time. The material is less important than where in the piece it has been put.