Maß or Mass is the German word describing the amount of beer in a regulation mug, in modern times exactly 1 liter. Maß is also a common abbreviation for Maßkrug, the handled drinking vessel containing it, ubiquitous in Bavarian beer gardens and beer halls, and a staple of Oktoberfest. This vessel is often referred to as a beer mug by English speakers, and can be correctly called a beer stein only if it is made of stoneware and capable of holding a regulation Maß of beer.
An empty Maßkrug
German Maßkrug of Augustiner Bräu
Patron's mugs stored under lock and key at the Hofbräuhaus am Platzl in Munich
A beer stein, or simply stein, is either a traditional beer mug made out of stoneware or specifically an ornamental beer mug sold as a souvenir or collectible. An 1894 article on beer mugs in the American Vogue magazine that describes various types of steins stated: "And it is to this [i.e. German] nation that we owe Wagner's music and the apotheosis of the beer mug."
Stoneware beer steins
A typical half-litre German Humpen (beer mug)
An unusually large German beer stein with a 32-liter (8.45 U.S. gal) capacity that weighs 16 kilograms (35 lb) when empty
Beer stein made in Poland