I guess we'll have to conclude that the "world of guitar" meanings of the terms are substantially narrower than those used by laymen.
In the interest of educating everyone: Tone is more like turning the bass and treble up or down on an equalizer. Contrast this with hearing an original version of a song and then someone else covering it and you'll have a good idea of how style is different from tone.
Equipment is precisely how you change tone, though there are possibilities for tone changes with existing equipment.
That does not, in the slightest bit, make it any less true. Whatever you want to call it, a persons personal ability has a very real impact on how they performa a specific task, independent of any equipment they use.
The point is to find the thing you are passionate about and DO THAT. Don't get caught up in trying to figure out the specifics of it. If you are good at it, none of that matters.