As I understand it, the are not the same. Similar but with differences. A pyroclastic flow is volcanic debris propelled by gases while a lahar is volcanic debris propelled by water. A pyroclastic flow is primarily composed of super-heated volcanic ash emitted at the eruption while a lahar is basically a mudslide comprised of ash, dirt, and water which begins to be created at the eruption but whose effects come later after the eruption. Pyroclastic flows kill through scorching or by toxic gases. Lahars kill by crushing those unable to get away from the cement-like slurry.
“they” not the in the first line.
My understanding is that the term pyroclastic refers to the mud. The mud is created by superheated gases (not necessarily ash) that is expelled in the eruption, which near instantaneously melts the snow and ice on the mountain that it comes in contact with, and mixes it with dirt as well as rock, trees, boulders and anything else in the eruption area. This becomes a very hot, viscous mud on an unstable hillside with the force of the blast propelling it.
Yes, there are gasses and high heat initially (and quite frankly, if the gasses and heat did not get you, the blast would), but the fine line you are differentiating is between the initial stage at eruption and the end stage (maybe 60 miles away) of the exact same flow of mud. Of course the heat will be lower downstream, and many of the heavier solids (boulders) will settle before making it to the end.
Lahars may crush, but they kill by consuming everything in their path. Around Mt Rainier, there are many examples of forests with nothing but dead treetops. The trees were not crushed, they survived the mud flowing around them, but died because unlike water, the mud never recedes and their roots are now 50-100 feet below the surface. A person caught in a lahar or pyroclastic flow (again, I hold they are the same thing) would be in a situation akin to trying to swim out of a very fast moving river of quicksand.
Note, as when St Helens erupted, you do see rivers overflowing their banks and carrying entire forests downstream ... but those are NOT Lahars. Those are caused by lakes being emptied and some melting of snow/ice and of course rain. The recent floods in TX were certainly not lahars, they were flooded rivers. I would challenge you to find a Lahar that did not start as a pyroclastic flow.
Final note. If you look up the term “Lahar”, it is a violent mud/debris flow composed of a slurry of pyroclastic material, rocky debris, and water.