It's the same bug. Kay didn't kill it, he just wounded it mortally.
Bug gets blown in half by Kay
Front half sneaks up behind Jay and Kay
This is backed up in the script
As they argue, behind them, unseen, THE FRONT HALF OF THE BUG RAISES
ITSELF UP on its forearms, eyes gleaming with hate, jaws dripping -- ready
to lower itself onto Kay and Jay.
JAY: After I got the shit beat out of me!
The film's Official Novelisation is a little more detailed, but basically confirms what's in the script.
Jay sensed rather than saw what happened next. Felt a sense of sudden
dread envelop him. Spun—
—saw the top half of the bug, levered up on its arms, mouth open,
about to fall on them.
Kerb dragged his upper half toward the humans. It was going to strain
his regeneration capabilities to their utmost to survive this one.
Maybe he wouldn't make it. Truth was, he didn't know any of his
species who'd lost their whole bottom half and come back, but he was
tough. There was always a first time.
Whatever, he had to kill these damned humans. At the very least, if he
was going to cross over the Bridge to the Other Side, he was not going
without the company of those who'd sent him there.
He lifted himself, opened his mouth. Now—!
Jay screamed, something wordless, and prepared to die—
Boom! The bug's head shattered, blew apart. Bits of chitin and brain
and circulating fluid splashed and pattered all over Jay and Kay,