The difference between metal sheet, plate, and foil is the thickness of the metal, with foil being the thinnest and plate being the thickest, but the boundaries vary depending on who you are talking to and the material you are talking about.

I believe the thickness limits developed from the use of a gauge number to specify sheet metal thickness, with metal thicker than the size range covered by the gauge standard being termed plate and metal thinner than the size range covered by the gauge standard being termed foil. A number of different gauges standards have been used for different applications. For example, gauges for ferrous metals (steels) are not used for non-ferrous metals such as aluminum and copper alloys, and there are also regional preferences for alternative gauges.

Depending on the historical application of the various gauges to describe sheet metal, and their thickness limits, or simply local practice, the thickness at which metal is described as foil, sheet or plate is different. Confusingly, the same gauge number refers to a different thickness in different gauge standards. Due to this potential for confusion, the use of gauge number is discouraged by current standards organizations such as ASTM, “as being an archaic term of limited usefulness not having general agreement on meaning”.

For a definitive answer, it is necessary to refer to a standard or specification recognized by the manufacturer of the metal product in question (so it does still depend on who you are talking to). For example, stainless steel can be purchased in compliance with the specifications of ASTM A480/A480M (08b) - Standard Specification for General Requirements for Flat-Rolled Stainless Heat-Resisting Steel Plate, Sheet, and Strip. This includes the following definitions for material complying with this standard:

Plate: material 5.00 mm and over in thickness and over 250 mm in width;

Sheet: material under 5.00 mm in thickness and 600 mm and over in width;

Strip: cold-rolled material under 5.00 mm in thickness and under 600 mm in width.

Note that the metric dimensions are not conversions of the imperial measurements: they are the measurements used by the metric version of the standard, ASTM A480M.

This does not mean that all stainless steel of thickness 5.00 mm and over must be called plate, but it is the correct term for material complying with this particular standard. Since ASTM A480/A480M does not include requirements for metal foil, it does not define a boundary between foil and sheet. A different standard would need to be specified for stainless steel foil, and this standard would define the thickness of material that is covered. Different standards would also need to be specified for other metals, and they may well define the sheet and plate thickness limits differently (for historical reasons, such as the gauge standard previously used).