Plumbing is any system that conveys fluids for a wide range of applications.
Heating and cooling, waste removal, and potable water delivery are among the most common uses for plumbing however plumbing's not limited to these applications.1 Plumbing utilizes pipes, valves, plumbing fixtures, tanks, and other apparatuses to convey fluids.2 Trades that work with plumbing such as boilermakers, plumbers, and pipefitters are referred to the plumbing trade.
In the Developed world plumbing infrastructure is critical for public health and sanitation.Źródło: https://en.wikipedia.org/wiki/Plumbing
A boiler is a closed vessel in which water or other fluid is heated.
The fluid does not necessarily boil.
(In North America the term "furnace" is normally used if the purpose is not actually to boil the fluid.) The heated or vaporized fluid exits the boiler for use in various processes or heating applications,12 including water heating, central heating, boiler-based power generation, cooking, and sanitationŹródło: https://en.wikipedia.org/wiki/Boiler.