Going back a bit further in history -
P&W's first production axial-flow engine, the J57, had two spools to permit matching the pumping of the front compressor stages to the rear. A single-spool fixed-geometry compressor likes to run over a narrow speed range, and two spools (w/ interstage bleed valves) was P&W's solution to the problem. The civil version was the JT3C; later a smallish front fan was added in the JT3D (a.k.a. TF33).
A bit later GE introduced the variable stator (variable geometry) system on the single-spool J79. And it didn't require bleed valves. Being a quite a bit lighter and capable of Mach 2 inlet temperatures, it competed readily with the J57 in the military market; but its civil CJ805 model saw few customers and its Convair jetliners didn't fare so well in the market.
As both companies developed their early high-bypass fans, their compressor technologies began to grow more alike. P&W added some variable stators on the JT9D, and GE found variable bypass (or bleed) valves necessary on the CF6-50.