Gold-plate is created using an electro-chemical processes.
Gold-filled, or gold-overlay, is created by heat-and-pressure-bonding a thin layer of gold to a brass core.
Gold-plate places a thin molecule of gold, or most often, something that really isn't karat-gold and which leaves a gold color, on copper or brass or some base metal. The gold color wears off pretty quickly when interacting with the wearer's skin salts or the pollutants in the air. Gold-filled places a layer of real gold over copper or brass or other metal. It wears off very slowly. For example, on a gold-filled ring, the gold-fill might wear off the inside of the ring shank after 3 years of constant wear, but remain on the outside of the ring for many, many years after that.
Note: I have just been corrected on my description of vermeil - and actually it never was "MY" description. However, the true definition of vermeil or vermeille is a specific thickness of gold plated over any sterling item whereas gold filled is a much thicker sheet of gold mechanically bonded to base metal, typically brass. When a jewelry designer or a company is manufacturing gold-filled jewelry, it is their choice as to how thick a layer of gold to place over the base metal material. Thus, you can have two gold-filled pieces, and you may have the gold layer wear off more quickly on one piece than the other. It is difficult, unfortunately, to be able to tell whether the purchase price of any piece reflects its true value. Sometimes, you will see a notation next to the Gold-Filled label indicating the relationship between the weight of karat-gold and the weight of the brass core material. For example, if you see the notion "14/20 Gold-Filled," this means that the piece is 1/20th 14 karat gold. The 1/20 notation refers to the ratio of the 14 karat gold layer to the brass layer by weight, which is 5%.
In any case, gold-filled is a much more durable product than gold-plate. Gold-filled jewelry is economical, and enjoys the rich look of gold at a fraction of the cost.