They are dialectal forms, but it could be said that three synonymous forms , , and have gained more or less nation-wide recognition today. The situation is somehow similar to that "soda/pop/coke" tripartition in USA.
The name of snail has been a signature of Japanese dialectology since the pioneering work written in 1930 by Kunio Yanagida. The summary of this book is that dialectal forms distribute in concentric circles from Kyoto, so that the remotest place maintains the oldest form.
> (newer/nearer to Kyoto → older/farther)
> > > > > (source)
A very detailed survey on word forms of "snail" conducted by was compiled into three atlas (No. 1, 2, 3) if you seek further understanding. (Tons of local forms recorded.)
I (and most people living in Tokyo) would use most often.