Speaking non-technically: recording can capture the guitar's beautiful sound, but not necessarily authentically. To put it another way, I can appreciate wonderful playing from recordings, but I'd probably never buy a guitar just from hearing a recording. I'd have to hear it live.
Guitarist Ed Gerhard (not a classical guitarist) made a record playing blues on "authentic" instruments; that is, the same kind of (and sometimes same instrument) guitars that original acoustic blues artists played for their own recordings (20s, 30s, 40s and beyond). Old, cheap, needing a set-up, not-necessarily-great steel string guitars. By and large they sound terrific on the recording! Much of this is Gerhard's own skill, and some has to be the recording environment.
2015 Connor spruce/Indian rosewood
1978 Ramirez 1a cedar