The term "Variac" (from "vary AC") has become generic, and commonly refers to any continuously variable autotransformer. Variac is a trade name, and has changed ownership several times since early 1930s when the device was first produced. Other trade names include Powerstat and Dimmerstat, and I'm sure there are many others. Some manufacturers simply call their versions "variable voltage transformers". The trade name Variac has been owned or licensed by Warburton Franki (in Australia), General Radio (Genrad), Claude Lyons, Statco and probably a few others as well. I shall use the term Variac (small "v") in its generic form - this does not imply that variable transformers with the Variac branding are more desirable than others, only that I'm used to the term having used it all my working life. 
The Variac is a special type of transformer, generally having a single winding and a single layer. The top section of the winding is flattened and machined to remove the insulation and provide a smooth surface for the sliding brush that's used to select the voltage needed. Some variations use a roller instead of a brush, but there seems to be no specific advantage. I still have my first Variac (branded as such) that I bought sometime around 1960, and it's been dismantled for service once in all that time - see Figure 1a. Figure 1b is a Matsunaga 1kVA Variac - made in Japan especially for use in Australia. It is described as a "Deluxe Slide Regulator" (sic).

The term "Variac" (from "vary AC") has become generic, and commonly refers to any continuously variable autotransformer. Variac is a trade name, and has changed ownership several times since early 1930s when the device was first produced. Other trade names include Powerstat and Dimmerstat, and I'm sure there are many others. Some manufacturers simply call their versions "variable voltage transformers". The trade name Variac has been owned or licensed by Warburton Franki (in Australia), General Radio (Genrad), Claude Lyons, Statco and probably a few others as well. I shall use the term Variac (small "v") in its generic form - this does not imply that variable transformers with the Variac branding are more desirable than others, only that I'm used to the term having used it all my working life. 
The Variac is a special type of transformer, generally having a single winding and a single layer. The top section of the winding is flattened and machined to remove the insulation and provide a smooth surface for the sliding brush that's used to select the voltage needed. Some variations use a roller instead of a brush, but there seems to be no specific advantage. I still have my first Variac (branded as such) that I bought sometime around 1960, and it's been dismantled for service once in all that time - see Figure 1a. Figure 1b is a Matsunaga 1kVA Variac - made in Japan especially for use in Australia. It is described as a "Deluxe Slide Regulator" (sic).