FREEPORT THERE are two men on the Island's South Shore who are known as Vinnie Fiore. Both of them have been in the shellfish business for 37 years - the kind of family-run partnership that is less common now than when they were younger men. One of the two Vinnies - the one whose birth certificate says his first name is really Fiorentino - can usually be found in their wholesale store in Freeport, selling clams bought from baymen by his brother, the other Vinnie Fiore, the one whose real name is Vincent.

In their years in the shellfish business, the Fiores have endured scare after scare about contaminated clams. But few such crises have troubled them as much as the one that began at Christmastime and that has since been described by state officials as the worst shellfish contamination problem in recent memory.

Now, with more than 800 people reported ill from having eaten bad clams, uncertainty about clams - any clams - lingers for consumers and for officials. Shellfish sales have stalled, and for the Fiores that has meant big losses, even though no one has got sick from eating any of their clams.

''We've lost over 25 percent of our business since New Year's,'' Fiorentino Fiore said from behind his counter. ''I've lost over $3,000 a week - a lot of money.''