If someone gets a traumatic injury and then either regenerates, or is magically healed, are there any telltale signs that the injury occured? If I amputate an arm does it grow back, or do I have a fully healed stump? Is there scarring on the wounded spot?

Scar formation wouldn't make sense if you're regenerating unless you somehow gained the regeneration after the scar process had happened.

One of my players plays a vampire who got her hand blown off with a called shot, she critically glitched a regeneration roll, so I said that one finger didn't grow back all the way. She got killed shorty after that, from the same NPC that shot her hand off. I don't know why some players equate regeneration to invulnerability.

I equate spirit possession plus channeling meta magic with a force 7 spirit to invulnerability (IMG:style_emoticons/default/smile.gif) . I generally just have regenerating critters either grow the limb back completely or else have to grab and reattach it, which ever provides a cooler or more frightening image to the players. "You blow his leg off with your assault rifle. Nice job. He falls down but grabs the leg and slams it into the stump in some sort of grotesque effort to reattach it. To your horror it actually works. Now he looks really pissed."
For added flavour have the baddie beat the runners with his own dismembered limbs.

Ahhh... Leper Quake...

Invulnerability? No, but it probobly is a much faster version of what we already see on some critters running around in the real world. Basically regenerating entire new limbs in a few weeks.

RW regeneration is still pretty limited. A few regens and the DNA starts having obvious genetic mutations. It's an "oh shit" procedure and isn't perfect.

Yep. It happens for basically the same reason we die of old age. RW regeneration is largely just accelerated aging.

never claimed to be a biologist lol; just providing an anecdote that some creatures have zero trouble regrowing limbs and we as human's cant.

There have been several recent threads discussing dietary requirements for ghouls (meat only), and thinking about how rare real meat is in the sprawl, and how the number of human corpses required to feed a ghoul family for any extended time would pretty quickly attract attention. So if a ghoul had a Heal spell, it might allow his family to thrive while staying under the radar. Capture just one squatter, chop off a leg for dinner, heal it, rinse and repeat indefinately. It adds a certain horror element as the 'cattle' humans have to suffer through daily amputations for their extended stay, with no relief in sight. I can imagine the runners stumbling into a ghoul underground enclave and finding rows of livestock cages reminiscent of the PETA videos, each filled with deranged stumpy humans.

No.
Only real Regeneration can propperly restore Limbs.
Everything else will leave a fully healed stump.

Shadowrunners on a mission in Asamando get caught by security guards. They're led away to temporary holding cells. The ghoulish mayor grabs the dove shaman and says "This is what we do: we will kill you, skin you, cook you, eat you, throw your bones to the devil rats and make a canoe out of your skin. What would you like as your last request?" The shaman is unable to cope with this news and has a nervous breakdown. He asks for a knife and slits his wrists, killing himself so that he doesn't have to face this horrible fate.

A few days later the ghouls are hungry again. The mayor comes back and pulls out the technomancer, and gives him the same spiel: "This is what we do: we will kill you, skin you, cook you, eat you, throw your bones to the devil rats and make a canoe out of your skin. What would you like as your last request?" As the brains of the group, the TM realizes that if they gave the mage a knife maybe they'll give him a gun and he might shoot his way out and escape. Unfortunately he forgot that as a TM he didn't have any points left to spend on automatics and couldn't hit the broad side of a barn. The rush and disarm him, and carry out their intentions with brutal efficiency.

A couple days after that, the mayor stops by and pulls the last runner out of the cage. The samurai struggles defiantly but is eventually dragged to the head honcho, who repeats his mantra one last time: "This is what we do: we will kill you, skin you, cook you, eat you, throw your bones to the devil rats and make a canoe out of your skin. What would you like as your last request?" The sam looks defiantly at the mayor and says "I want a fork!" The ghouls are dumbfounded by this odd request. "We'll give you whatever you want, but you only get one request" says the mayor, "are you sure you want to waste it on something silly like this?". "A fork, dammit, give me a fork!" demands the street sam.

When they give the sam a fork while wondering what will happen next. The samurai clenches the fork in his fist and stabs himself all over his chest and torso, shouting "FUCK YOUR CANOE!"...

The lowest floating rib can regrow if you leave the attachment, the tip of the tongue (like 1/2 inch or shorter) can regrow, and most of the liver can regrow. Neat facts.

Also I never viewed Regen as a limb regen - just a faster healing method. It hasn't really come up in a game yet though.

Well with regen if you still had the leg and "reattached" it, wouldn't that take less time to regen than growing an entire new limb? After all, it's just reestablishing tissue connections.

I guess you could make a metaphysical argument against that, but if we can surgically reattach limbs today that have been severed for some time, a creature that could regen probably could pull his leg/arm back to his body and reattach it more quickly.

Also, it's good to know that while regen makes you tougher to kill, it really doesn't do jack for your pain threshold tolerance. Even if a creature had troll-like regeneration (cut off a limb and it grows back a few minutes later), the pain of cutting a limb off would possibly be blackout-inducing.

The sams in my game would probably have gone, "OK... you can kill me, but I hope you have a good recipe for plastic."

Hehe, that's kind of what I was thinking. Also that the fork would break on the sammy's dermal plating and would likely lack enough skin to make anything out of in the first place.

You mean like newts?