This section is from the book "Principles And Practice Of Plumbing", by John Joseph Cosgrove. Also available from Amazon: Principles and Practice of Plumbing.
Soil stacks are those that receive the discharge from water closets and urinals, although they may also receive the discharge from other fixtures. They connect with the house drain in the cellar or basement, and extend to a suitable point above the roof.
Soil Pipes are the branches that connect closets or urinals with soil stacks.
Waste Stacks receive the discharge from fixtures other than water closets or urinals. They also connect with the house drain and extend to a suitable point above the roof.
Waste Pipes are those that connect any fixtures other than water closets or urinals with either a waste stack or a soil stack.
A Vent Stack is a special ventilating pipe that connects with a soil or waste stack below the lowest fixture and extends to a point above the highest fixture, where it may again connect with the stack or extend separately through the roof. No soil or waste matter discharges into this pipe. Its function is to provide a supply of air to the outlets of fixture traps, to prevent the water seal being broken either by siphonage or by back pressure. That portion of soil and waste stacks above the highest fixtures may be considered as vent stacks.
A Vent Pipe is a short branch extending from the vent stack to the trap it ventilates.
 
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