Both versions work the same for the dying condition in that reaching dying 4 = death. Both allow recovery checks reach round, with some pretty key differences:
Core Rulebook
Recovery Checks
When you’re dying, at the start of each of your turns, you
must attempt a flat check with a DC equal to 10 + your
current dying value to see if you get better or worse. This
is called a recovery check. The effects of this check are
as follows.
Critical Success Your dying value is reduced by 2.
Success Your dying value is reduced by 1.
Failure Your dying value increases by 1.
Critical Failure Your dying value increases by 2.
Player Core
Recovery Checks
While you’re dying, attempt a recovery check at the start
of each of your turns. This is a flat check with a DC
equal to 10 + your current dying value to see if you get
better or worse.
Critical Success Your dying value is reduced by 2.
Success Your dying value is reduced by 1.
Failure Your dying value increases by 1 (plus your wounded
value, if any).
Critical Failure Your dying value increases by 2 (plus your
wounded value, if any).
Both versions have you add 2 to your dying value if you take damage from a critical hit while rolling recovery checks or 1 if you take damage from a regular hit. Both versions note to add your wounded value to that number.
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