Don't overthink it! It's a bit of fun not a scientific experiment.
I couldn't swear to tell a start from telecaster by its sound, but plenty of times I've recognised guitarists like Hendrix, Clapton or Billy Gibbons on a recording, often in odd contexts, like Clapton on 'Think I'll Go Back Home', a Steven Stills track. And I can be fooled by imitators, like SRV doing Hendrix.
So someone's 'signature' sound is rather like their voice. They can disguise it and others can imitate it*, but some people have one distinctive enough to be recognisable.
*Chetaing is easy. I've got an Ibanez '335', plenty of gain, bridge pickup and back off the tone -bend a few pentatonic licks and you get instant Clapton. Or use a modelling amp...