The word snail was a common name that was used for almost all members of the molluscan class Gastropoda which had coiled shells in the adult stage. Those snails which did not have a shell or only a very small shell were usually called slugs. One specific type of snail was the garden snail. Due to its slowness, the snail was traditionally seen as a symbol of laziness.
William T. Riker referred to an Earth nursery rhyme, "What Are Little Boys Made Of?", which stated: "Girls are made from sugar and spice, boys are made from snips and snails and puppy dog tails" to describe the "old-fashioned way of looking at the sexes" to the androgynous Soren. (TNG: "The Outcast")
Snails and other such mollusks were Ferengi delicacies. When Nilva visited Deep Space 9 to talk about Grand Nagus Zek's future and females wearing clothes, Zek suggested they discuss the matter over snail steaks. (DS9: "Profit and Lace") Later, when stranded with Odo on a planet, Quark lamented the lack of slugs there, as well as beetles, worms, and snails. (DS9: "The Ascent") Snail juice was also a common Ferengi beverage. (DS9: "Bar Association", et al.)
When the Hirogen subjected the crew of the USS Voyager to a simulation of World War II, Commander Chakotay and Lieutenant Tom Paris were led to believe, via the use of neural interfaces, that they were part of the US 5th Armored Infantry. Paris, as Bobby Davis, noted that there hadn't been any word yet from the French Resistance forces in Sainte Claire, but said not to underestimate them, noting he had spent a summer there when was eighteen. Chakotay, as Captain Miller commented "Let me guess. You ate a few snails, fell in love with a local girl and became an expert on the city." (VOY: "The Killing Game")