So... there are inconsistencies in terminology and depiction.
Quite true. But this is also true of the real world: we use inaccurate and downright false terminology to describe the functioning of everyday equipment, and this does not create a universe-terminating inconsistency or invalidate the equipment.
If terminology and depiction are at odds, we can safely choose the latter as authoritative in all cases. The transporter evidently raises passions, and may well have earned a reputation as molecule scrambler and taking-apart-machine that is difficult to shed even if this has nothing to do with the actual technical characteristics of the machine.
Timo Saloniemi