I think you may have two words mixed up: rmś and šrṣ.
Gen 7:21 states that all flesh died, including:
birds, livestock, beasts, all swarming creatures (šrṣ) that swarm on the earth, and all mankind.1
This is restated in 7:23, which says that God blotted out,
every living thing that was on the face of the ground, man and animals and creeping things (rmś) and birds of the heavens.
As you can see, the word normally translated “swarm" is from a different root (šrṣ) than the one normally translated "creep" (rmś).
Both rmś and šrṣ have verbal forms (rāmaś and šāraṣ) and noun forms (remeś and šereṣ) (contra another answer here). The first definition of the verbal form of rmś in BDB, a classical Hebrew lexicon forms the basis of translation of Gen 7:23 above:
creep, move lightly, move about.
This stands in contrast to šrṣ:
Based on this and the mention of both groups, it would seem two different groups of animals are in view. However, there may be overlap in some usages. For instance, see Gen 1:21 where God created,
every living creature that moves (rmś), with which the waters swarm (šrṣ).
This usage of rmś is described in BDB entry 2b (scroll down to page 943):
move lightly, glide about, of water animals.
It was mentioned in the comments that the question may also be wondering about the KJV's translation of 7:21 of šrṣ as "creep", i.e., the converse of the overlap mentioned above. This sense is not mentioned in BDB. HALOT, a more recent lexicon, does offer this possibility for the verb ("creep"), although not for the noun ("swarm").2
I suspect that the KJV translators were bothered by the idea of a "swarm" occurring on the earth, as the English term may be more suggestive of something in the water or sky.3 The noun used in 7:21 is a collective singular, though, an idea which is probably better expressed used the English "swarm" (even if it stretches the habitat normally associated with that word), hence most modern translations.
1. All translations are ESV.
2. Interestingly, HALOT calls 7:21 an "etymologizing expression", suggesting that the author intended to connect šrṣ with ʾāreṣ (earth) later in the verse: haššereṣ haššōrēṣ ʿal–hāʾāreṣ = "the swarm (šereṣ) swarming (šōrēṣ) on the earth (ʾāreṣ).
3. There may also be some influence from the Vulgate here: reptilium quae reptant.