The Billiard and its Variants
Billiard, Lovat & Liverpool
The billiard is characterized by a fairly cylindrical bowl, canted very slightly forward, with a round shank, roughly as long as the bowl is tall, and either a tapered or saddle stem that makes up roughly half the overall length of the pipe. The Lovat is similar to a billiard, with a slim shank that is 1.25-2 times the height of the bowl. The Lovat is always fitted with a short saddle stem. A Liverpool can be thought of as a Lovat with a tapered stem.
Pictured above, from top to bottom, are: Large Billiard (Dunhill LB), Billiard (Ashton Pebble Grain XX), Army Mount Billiard (Barling Ye Olde Wood Fossil EXEL), Lovat (Ashton Pebble Grain XX), Liverpool (a very old GBD Virgin)
Canadian & Lumberman
The Canadian is characterized by a billiard-like bowl, a long oval shank (typically about twice the bowl height) and a short, tapered stem. I have seen examples of pipes which are in every other regard a Canadian, but with a saddle bit fitted. Some will insist that this is not a Canadian at all. Since there is no accepted nomenclature for such a pipe, I simply refer to it as a saddle bit Canadian. A Lumberman is similar, but with a round shank, and a longer stem, often cut as a saddle bit.
Pictured above, top to bottom, are 2 GBD Canadians (Virgin, and Speciale with amber stem) and 2 GBD Lumbermen (Virgin and Prehistoric), in this case, with saddle stems.