Paul separates two things we routinely confuse. Godly sorrow brings repentance that leads to salvation without regret. Worldly sorrow brings death.
Both feel bad, which is why they get mistaken for each other. The difference is what they produce.
Worldly sorrow is mostly about consequences and self image. It is the sinking feeling of having been caught, or of no longer being able to think of yourself as the sort of person who does that. It generates a great deal of misery and no movement. You can circle it for years.
Godly sorrow moves. It results in repentance, which simply means turning, and Paul says it leaves no regret behind it.
That last phrase is the test worth applying. If the sorrow is producing a turn, it is doing its job. If it is only producing more sorrow, it is not repentance however awful it feels.
Feeling terrible has never once been the same as coming home.