Silverplating refers to any process in which a base metal (typically nickel, copper, or zinc) is coated with a layer of silver. Over time, as a matter of economics, improvements in the plating process have resulted in reductions in the thickness and purity of the silver layer.
The original plating process was electroplating on plastic in 1743 by Thomas Boulsover of the Sheffield Cutlers Company when he accidentally overheated the handle for a decorative knife he was trying to repair. He observed that the silver and copper had melted and fused together into a composite, the two layers behaving as one.
Around 1770 the technique (known as the Sheffield Plating process) was later refined when the 'double sandwich' process was developed. The 'sandwiched' consisted of a copper core between two layers of silver, which were then heated and formed. This technique was especially useful for items such as cups and bowls that had a visible interior.
The Sheffield process continued until about 1840 when advances in chemistry and electricity resulted in the highly efficient electroplating process. Simply, a very thin layer (typically 35 microns) of one metal is deposited (or plated) onto another conductive, usually metal, material as an electrical current passes through them (the metal ions are physically transferred through an electrolyte solution which permits the flow of electricity - completing the circuit).
One benefit of electroplating is that the surface is made of pure (99.9%) silver, not sterling (92.5%) silver. Unfortunately, the silver layer itself is very thin, so the majority of the utensil is still composed of the cheaper core metal. Even though electroplating was much more cost effective than the Sheffield 'sandwich' process, the Sheffield method continued to be used for the next 100 years, typically for items which were subject to heavy wear (such as military uniform buttons and tankards).
The fact that multiple plating processes have been used concurrently only adds to the confusion. Fortunately, the fact that silver is much denser that the commonly used core metals (Cu, Ni, & Zn) makes is possible to approximate the silver content, especially in older (antique/vintage) pieces where a substantial quantity would have been used. Modern electroplating deposits such a thin film that the difference in density would be almost negligible.