You asked if the expansion properties of foam is related to construction of the foam-making equipment. The answer, briefly, is 'Yes'. It is some years since I worked on foam at the Fire Research Station, but as I recall:
(a) Low expansion foam: Produced by a nozzle with two or more holes producing jets which hit each other to form a course spray inside a tube. The spray induces air into the foam, the tube directs the foam thus produced towards the fire.
(b) Medium expansion foam: Spray nozzle produces a finer spray, possibly impinging onto a mesh screen of some sort; this induces a greater volume of air to increase the expansion, but at the loss of much forward momentum so that the produced foam is not projected very far.
(c) High-expansion foam: Extra air is forced mechanically by a fan into a mesh (often plastic netting) onto which a foam solution is sprayed; this blows larger bubbles than is possible in (a) and (b).
Fire Service Manual, Volume 2, Firefighting Foam, contains a lot of information on foam equipment and may be of use to you.
Sorry I havn't written before, but this aspect of FireNet was only shown to me today!