I believe that "compact geometry" may have been a marketing phrase to describe the compactness of the front triangle of a frame when using a sloping top tube. Often used by designers to get a better standover height for a given frame size and sometimes touted as providing a stiffer frame (notice how marketing uses the same word to appeal to Freds and OCP'ers)

Relaxed geometry usually is used to mean more rearward lean in the steering tube (think chopper bike) which will make the bike more stable in a straight line but less responsive to steering input.

Marketing people however can change the definition of a phrase with but the firing of a single neuron thus leading to all sorts of theories about what they really mean. The best side effect of this is to provide hours of entertainment on 50+

And for Big Paulie...............yes.