Rikka, the "manifold" is usually called the plenum or flue transition.
Here's a thread about it i tried to start.
https://permies.com/t/61657/Flue-exhaust-transition-plenum-pictures
Regarding system size, as Glenn explained, it's usually stated as the diameter of the pipe used. Which gives you a "CSA" or cross sectional area. Which should remain constant, except in the plenum. Usually the minimum accepted number there, is 1.5 times CSA, best practice is to reach, if possible, for 3 times CSA, ass ashes love to pile up in there.
System size, also gives you the maximum length of pipe you can useOr the biggest ISA for bells.
HTH.
Max.