The first flamethrowers date to the 7th century. No they aren’t modern military flamethrowers but as with the description “commercial flamethrowers are generally blowtorches using gaseous fuels such as propane”. No they don’t have the same range or lethality but saying they cant both be flamethrowers is saying a BB doesn’t shoot projectiles because it’s not as the same projectiles and range of a military assault rifle.
Not all flamethrowers throw napalm, as seen flamethrowers predate napalm. A flamethrower made to abate weeds is not nearly as powerful as a military grade one, but it still throws flame. So even if you can’t buy a fancy flamethrower that shoots out 20+ feet, you can have some fun with a little propane tank based weed abatement “flamethrower”. I wasn’t trying to kick up an argument on the technicalities of what is a flamethrower, but your arguments are the weakest thing to support your idea.