Question

Hello Rabbi,
Is it also permitted, according to those who allow lighting a match on a Jewish holiday because “since there is sulfur and combustible material on the tip of the match, this is considered as though the fire is already present in the match, and rubbing these materials together does not constitute creating fire, so it is permitted on a Jewish holiday,” to do so with a lighter as well? (It sounds a bit strange to me, but since some people practice this way, I wanted to know whether this argument is supposed to apply to a lighter too.)
Thank you!