Foil Stamping or Foil Printing goes by lots of different names, and there are a few different ways of achieving it.
Foil Stamping or Hot Foil Stamping is essentially Letterpress printing using foils instead of inks. If you are not familiar with the letterpress process, it uses a raised printing plate which is inked, in foil that plate is heated, and in both processes the plate is forced with tons of pressure into the paper. Lollipop uses both of these in creating our Invitations and Stationery.
Foil Printing is more of a generic term and can refer to another foil process in which toner is printed on the paper and then heat is used to fuse the foil to the toner and paper. We do not use this process and prefer the look and feel of hot foil stamping and letterpress.