Rummaging through the official novelisation, mostly we just see bullet-firing "guns", "rifles" and "pistols". Occasionally there's mention of sci-fi-y "pulse-pistols" and "heat-signature rifles" which seem to fire the plasma rounds that Snyder mentioned, but without any obvious description of how they work or what they're firing.
Bodies lay where they fell. Viscera and blood saturated the ground.
She hesitated to go farther, seeing a group of people from the town
pointing long-range pulse pistols and heat signature rifles to the
sky. The staccato of rapid fire overhead made her cover her ears
again. Each of those people fell dead with multiple shots to their
bodies. There was no way to outrun whatever killed them. When the
threat was gone, she began to move again, but a pistol in the hands of
a bloating dead man caught her eye.
Rebel Moon: Official Novelisation
The 'making-of' book goes more into detail about how the plasma-firing rifles might work.
"Our main motherworld rifle, for example, was designed with this
really cool bit of technology on top - Nobody knew what that was.",
[Prop Master Brad] Elliot recalls. "Our guns shoot this burning piece of dense plasma,
like a chunk of lava the size of a cork. If it hits you, it would
probably make a hole in you and knock you over. My first thought went
to 'They're going to get hot. We're going to need to dissipate this
heat. So a lot of the gun design is focused really on heat sinks. That
little top chunk that we had on the AR [Assault Rifle] is now
something that's going to reciprocate back and forth as if it's
cycling some coolant into the barrel or if it's a radiator fanning
itself".
Rebel Moon: Wolf: Ex Nihilo: Cosmology & Technology
and
Brad Elliot: No, we have a really interesting sort of idea for that.
It's all like tanks of plasma. This is going to light up for us. So
this is one that's fun because when you load it, you get all the ammo
counters and then as you shoot it, they go away…So what we shoot is,
think of it as a lava cork. It's molten, it's heavy, and it's about
the size of a cork. So if it hit you, it would knock you over, but the
hole that it would create would cauterize, if that makes sense. If it
hits a hard surface like metal, it's going to hit and maybe drip a
little bit, like a lava would, if that makes sense. They're either
driven by these sort of tank-like magazines, and when I say tank, it
means there's a pressurized sort of plasma inside of them. Or when we
get to Veldt and we get to their hunting weapons, they're a little
older, so they go on like a, it's still caseless, but it's like a puck
of whatever this compressed material is that would then become what
that is.
Rebel Moon Set Visit Interview With Prop Master Brad Elliot
The brightly lit swords are just referred to as "swords" or "oracle-steel sword", although there's a fair bit of explanation how they work.
One of Harmada’s stinging, sharp-tipped legs stabbed toward Nemesis.
The warrior swordswoman lunged out of the way to avoid being skewered,
but her left arm was grazed. Harmada’s leg had ripped through cloth
and flesh. In an instant, Nemesis drew her swords, raised them to
protect herself from a still-stabbing Harmada. The furious creature
shrieked before swiping again. The tip of a leg went straight through
one of Nemesis’s gloves. The energy within crackled. This time Nemesis
did not hold back.
Her swords became imbued with the power of the ancient blood and
wisdom of her ancestors. And that blood took the form of molten lava
heat that dwelled within the swords. They glowed brighter like
seething rage as the heat radiated from the center and spread across
every inch of metal. The brightness of the fires of Byeol could be
seen as they were prepared to strike a foe. She placed both in front
of her and drew an incandescent circle around her with the heated tips
of the swords. When Harmada struck again, Nemesis was ready and sliced
the air with her left sword. One of Harmada’s legs flew into the air,
releasing squirts of viscous greenish blood. She cried out in agony
and dropped the child.
Rebel Moon: Official Novelisation
The baddies also have these swords, presumably raided and repurposed. They need external powerpacks to power them and can only hold them with special heat-dissipating gloves.
For close combat, "They have their oracle-steel swords that are
externally powered," Snyder explains. "There's a little power unit on
them. Clumsy wiring, crude. Those are unlike Nemesis's swords which
are made of the same kind of metal but are more elegant because the
power source is her. She's more in harmony with her swords. The
Krypteians have had to retrofit and glue things on to make them work,
and so they defile the beautiful symmetry of the thing. That's why
they wear those gloves, so they can hold the sword. It's kind of like
an oven mitt".