Well, that's a tricky question. "Back in the day", most of the "big" apparatus manufacturers made both pump and body (and heck, even the engine, until the '30s-ish). Ahrens-Fox, Mack, Seagrave, and American-LaFrance all made everything from stem to stern through the '20s and 30s. Eventually, most went to an outside engine provider, or bought the rights to a 3rd-party designed truck (American LaFrance bought and repurposed an Allison - or Lycoming? - V12, Seagrave bought and slightly modified the Pierce-Arrow v12. Mack actually stuck with their own engines right up until they stopped making fire apparatus.
Pumps were somewhat similar. Ahrens-Fox and American-LaFrance were famous for their piston and rotary gear pumps. Seagrave was the first with a centrifugal pump, all bronze. Eventually, Waterous & Hale became the predominant suppliers.
Other pump makers? Well, you mention Darley. Their champion pump was a popular front-mount through the '40s. And Darley made truck bodies and equipment as well, though I think they always used a commercial chassis. They were a large, catalog sales company from very early on (the teens, I think).
And of course, my beloved American Fire Apparatus was a division/spin-off of American-Marsh Pumps, responsible for the Barton centrifugal pumps, both front-mount and mid-ship. Their "Duplex-Multistage" pump was an ingenious design, absolutely unique in the industry. American made whole truck bodies and equipment as well, like Darley.
And yes, Darley is absolutely still in business (check out "EDarley.com"), selling equipment, pumps, and trucks.
Nope, American Fire Apparatus is NOT in business any longer (sob sob, sniffle sniffle . . . ).
Did I get it right?
-Michael