Your electric guitar is really just half of the story. Much of the character of the sound you produce is down to your amp. Particularly old fashioned valve technology, which adds warmth and artificial harmonics to the basic tone of your instrument.
British amps like Vox and Marshall have pioneered the rock and pop scene since the 60’s. Fender have been around even earlier (since the mid 40’s). Though there are now a plethora of excellent boutique amps from smaller manufacturers, arguably the last modern amp to be sought after for it’s distinct signature tone was the Mesa/Boogie mark series.
These amps in conjunction with the classic Fender, Gibson, Rickenbacker and Gretsch guitars are responsible for most of the sounds you’ve ever heard live or on record.