"I thought long stoke vs. short stoke is based on how far the piston moves before the gas vents, not how long the rod/piston is or if there is an intermediate rod."
I think both definitions are correct, but this one has become outmoded. Long stroke, in automotive piston applications, actually does have to do with the proportion of piston travel driven under pressure before venting, and I suspect the initial firearms nomenclature mirrored this.
But firearms design subsequently fell into essentially two camps, most clearly differentiated by whether or not the gas-impinged piston head was hard-linked to the bolt operating device. Since no one knows, or is expected to know, the displacement of a given piston before it vents, the earlier description isn't really that useful in conversation. But the prevailing description detailing piston attachment is very descriptive when it comes to discussing or comparing different designs. It provides a starting point that puts everything into two buckets, instead of a continuum of multiple variables (like we have for cartridges. Just imagine the .5" vs. .505" driving distance debates we could be having! What fun!
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Long Stroke:
-Generally more aggressive operation (this is more the cause of increased recoil than anything)
-Tend to be overgassed (the extra reciprocating mass can absorb the extra energy without speeding up so fast it overrides the magazine and jams) for marginal reliability boost
-Tend to be simpler (the parts count and receiver designs, anyway)
-Tend to be more easily tuned (more fixed variables)
-Tend to have smaller bolt & carrier contact surfaces in the receiver (the gas tube can act as a primary guide)
-Slower cyclic speed (can be a blessing or a curse, depending on requirements)
Short Stroke:
-Intermittent recoil impulse (piston returns separate from the carrier, which can counteract each others' impacts; people used to AKs hate the felt difference, and vice versa)
-Tend to be self-regulating (regardless its violence, the pressure impulse can only drive the piston so far before being completely cut off)
-Tend to have more complex receiver rails or bolt carriers (since the piston cannot guide the carrier)
-Higher parts count (usually an extra spring, but that's usually it)
-usually better ejection port access (no piston in the way once retracted)
I'm no expert on AR conversions, but to be honest the tubular bolt carrier design of the platform is non-ideal for either (but especially the short stroke since there are no small contact areas to control up/down pitch, only broad surfaces inside the receiver tube with lots of opportunity to exert friction). That's not to say it doesn't work, after all, the HK416 is highly regarded, but obviously it's taken a whole lot of time and energy for anyone to export the initial success of the AR180 into the tubular AR chassis (I honestly wonder if a modern re-visiting of the VZ52 annular piston in a world of non-corrosive powders might be in order; that gun had a cylindrical carrier after all, and was quite reliable if corrosion was kept at bay)
TCB