Book 3 is rather out of date - although I understand the Foam section has been reissued as part of the new fire service manuals.
The extinguisher bit in the pump is very obsolete & as for stirrup pumps.....
I always understood that there were two types of making foam - chemical by the reaction of seperate powdered chemicals (bicarb/saponin with aluminium sulphate) & concentrate where the foaming agent is one concentrated solution to be inducted into water for deliver as aspirated or non aspirated finished foam.
The concentrate form has been called various names such as mechanical foam, "air" foam, etc.
Yes you have varying ways of applying foam - N-A, LX, MX & HX and via branch, monitor, pourer, sprinkler, base injection.
Plus there are now many types of concentrate, the traditional P, FP, AFFF & FFFP with their -AR counterparts have a myriad of new compounds and application methods an example is compressed air foam.
A very good starter reference to Foam is the Angus Foam Handbook if you can borrow a copy. I don't know if they still produce it, but even if not they still produce a lot of useful reference some linked via their WWW
