"Step" refers to an interval gap of "half step" or "whole step". In a way, I could see this as a "specific meaning", but since it refers to a group of intervals and not a single one, I would be quite open to a definition where '1 step' is always '1 half step', since both 'semitone' and 'half step' imply a less useful fundamental value of 2 half steps, even though music that involves only whole steps is quite dissonant and uncommon (the whole tone scale).
Your entire hypothetical dialogue is confusing as well, since your hypothetical person isn't using correct words either. The situation where C + 6 of something = B is with scale degrees (C moved 6 scale degrees up is B). And then you say "I currently mean tones", when 6 "tones" has the exact same grouping problem you are criticizing (because 'whole tone' and 'semitone' have the exact same meaning as 'whole step' and 'half step', only now 'scale tone' is in the group too). This artificially lengthens the example.
"The tritone of this note is 6 steps up" "Gotcha, so the tritone of C is B" "No, that's scale degrees, by 'step' I mean 'half step'." "Oh, so it's F# then." Done.
Your entire hypothetical dialogue is confusing as well, since your hypothetical person isn't using correct words either. The situation where C + 6 of something = B is with scale degrees (C moved 6 scale degrees up is B). And then you say "I currently mean tones", when 6 "tones" has the exact same grouping problem you are criticizing (because 'whole tone' and 'semitone' have the exact same meaning as 'whole step' and 'half step', only now 'scale tone' is in the group too). This artificially lengthens the example.
"The tritone of this note is 6 steps up" "Gotcha, so the tritone of C is B" "No, that's scale degrees, by 'step' I mean 'half step'." "Oh, so it's F# then." Done.