Churchill's personal plane was an LB-30 (export version) of the B-24 and was called Liberator II by the British. Eventually 87 LB-30s served in the RAF. Churchill's personal LB-30 was named “Commando”.
The Liberator II was the first version of the B-24 to feature the lengthened nose that would become standard on all later aircraft. This extension, which increased the length of the aircraft from 63ft 9in to 66ft 4in, was originally made for purely aesthetic reasons, but as the war developed, and the amount of equipment carried on aircraft increased, the extra space proved to be very valuable.
The Liberator II was powered by commercial Pratt & Whitney R-1830-S3C4-G engines. These engines lacked the turbosuperchargers used on USAAF B-24 aircraft. The P&W engines turned Curtiss Electric propellers (longer propeller hubs) than the more common, shorter hubs, of the Hamilton-Standard propellers found on the B-24.
In RAF service, the LB-30 carried 14 .303-inch machine guns: one in the nose, one in a tunnel hatch, two in each waist position, and four each in Boulton-Paul power operated tail and dorsal turrets.
IIRC, the B-24 and the China Clipper shared the same wing design (and its high placement, which, of course, was ideal for a flying boat)...
Otherwise, as you say, "apples to oranges"...