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 layer of gold, or most often, something that really isn't  karat-gold which leaves a gold color, on a base metal.  The gold color wears off  pretty quickly when coming into contact with the wearers skin and environment.

Gold-filled places a layer of real gold over a base metal.  It wears off very slowly.  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 a very long time after that.

When Gold-Filled is over sterling silver, the finish is called Vermeil.  Because the gold does not adhere fully to the silver, the silver continues to tarnish under the gold.   Any vermeil piece will darken with age.  

Gold-filled is a much more durable product than gold-plate or vermeil.  Gold-filled jewellry is economical, and enjoys the rich look of gold at a fraction of the cost.

NOTE:
All the pieces found on this site are 14/20 Gold Filled which means 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%.   What is important here is not the content of gold, but rather more the color of the gold-filled piece.  14/20 Gold Filled will be more golden, darker, mellow.   12/20 Gold Filled will be brighter, brassier, yellower.