Rank

Upon completing a level, you are awarded a Score and also a letter rank which represents your performance. Your rank is dependent on score, knockdowns, and Combo drops.

Rank is not important for the purposes of leaderboards, since leaderboards are ordered by score only (except for Infinity Drive and Daily Drive which are ordered by completion layer, then score). The highest-scoring runs are often incidentally going to be S+ anyway, since you always want to keep up Combo for score purposes.

Pro Mode
Getting an S+ rank in any level unlocks Pro Mode. In the options, you can enable an S+ indicator which appears to the left of the battery. If Combo drops at any time, it will smash with a loud noise and sparkly visual effect, indicating that this run is no longer eligible for an S+ rank.

You can also opt to automatically restart when the indicator is smashed, which is accompanied by a unique black-and-white screen filter.

If auto-restart is on, the S+ indicator appears purple. If not, it appears blue.

Pro Mode also grants access to the quick-restart shortcut (Select on most controllers, R on the keyboard)

Corner case: Dropping combo, but still receiving an S+ rank
If at the end of a level, you drop Combo but the remaining enemies die to each other (or environmental damage), you still receive an S+ rank.

This is because the real criterion for S+ is that your kills is equal to your maximum combo (and you have no knockdowns)