Hey Harley, I spose the simple answer is yes and no. There are so many variables to account for/balance. If what you mean is the guitar speakers sound one way to your ears but when that's recorded (and then how was it recorded (vast array of how, e.g. mics, mic placement, I/O device, software/tape, levels....) it sounds different.
There are lots of reasons a guitar rig may sound different recorded, however, from your question, the main one that come to mind is mic proximity effect (and very much depends on the mic). If you use say SM 57s (popular choice for miking guitar cabs), 57's and 58's were designed to have a distinct bass boost when up close to the source, they also both have a 5khz (presence) boost (hump).
If you really want to try to capture exactly (well as close as you can get) to what's coming off the speaker, you'd use a high quality condenser mic(s) and not too close (so not to overload it/them, or bottom out the diaphragm (distortion/blah...) and give the wavelengths (particularly low end) time/space to develop (e.g. low bass notes are 32 feet long in the air)). In a studio scenario, I'd chase down the capture like every other instrument to get the best from what I have to work with.
I tend to record direct from MP2 cab sim outs into ProTools, but I monitor through the studio monitors so what I play (hear) is much what I get when I play it back. I also have my system set flat, no eq to the speakers. When I hear live recordings of my rig (again so gear/mic and expertise dependent (and mostly cam corders these days (so not great audio))) it sounds very different, for me typically more toppy than I'm hearing (and what you hear on stage depends where you stand with regard to your cabs, and partly why RabbidGerry experimented with foam in front of the speaker cones to disperse the sound better (he hates the "beaming")).