Two rings can look identical in a photo and differ by a factor of fifty in price. The difference is how much gold there is, and where.
Solid gold
The piece is a gold alloy all the way through, for example 14 or 18 carat. Nothing can wear off, because there is nothing underneath. It can be polished, resized, repaired and eventually melted down into something new. It is stamped with its fineness, such as 585 or 750, see hallmarks. "Solid" says nothing about the carat: 9 carat is solid gold too, with less gold in it. See gold: carat and alloys.
Gold vermeil
Sterling silver with a layer of gold over it. The base is a precious metal, so the stamp reads 925. In the United States the term requires a gold layer of at least 2.5 microns. Elsewhere the word is used more loosely, so ask how thick the layer is.
Gold-filled
A thick layer of gold bonded by heat and pressure to a base metal, usually brass. Under the American standard the gold must be at least one twentieth of the total weight, marked for example as 1/20 14K GF. The layer is many times thicker than plating and lasts for years, but it is still a layer.
Gold-plated
A very thin layer of gold deposited on a base metal, often brass. Marks such as GP or HGE indicate it. The layer is usually thinner than one micron and wears through at the places that rub: the underside of a ring, the clasp of a chain. When the base metal is exposed it can discolour and irritate the skin.
Why it matters
Wear. Every layer wears off eventually. How soon depends on its thickness and on where the piece is worn. Rings wear fastest, earrings slowest.
Repair. Plated and filled pieces can hardly be resized or soldered: heat and polishing destroy the layer. A solid piece can be repaired again and again.
Value. A layer of gold has practically no material value. A solid piece always keeps the value of its metal.
Skin. If you react to base metals, a layer protects you only as long as it lasts.
Independent goldsmiths work mainly in solid precious metal, because it can be forged, soldered and repaired. If a listing does not say, ask: solid, or a layer?