Cap. James Bruce Saxon Jr. had just cast his shrimp nets in a disputed area of the Savannah River one day recently when two visitors boarded his 62-foot shrimp trawler, the Rebel.

The visitors, Georgia game and fish wardens, accused the South Carolina captain of shrimping legally in waters claimed by Georgia, which had not yet opened its shrimping season.

The 29-year-old Saxon was ordered to sail into a Georgia harbor, where his boat and shrimp catch would be confiscated and he and his two mates jailed.

But the husky former football player headed instead for the safety of waters that were indisputably in South Carolina. The Georgia officials, their .38-cal. pistols still in their holsters, went along as startled passengers.

When the Rebel docked at Hilton Head Island, the Georgia wardens were left to find their own way home.

Back in Georgia, the wardens filed an array of charges that have swept James Bruce Saxon up in a modern-day version of an old-fashioned kind of conflict; a border dispute. And the stakes go far beyond Saxon and his shrimp boat - at issue is government money, millions of dollars' worth.

Under the Costal Zone Management Act of 1972, as amended in 1976, the federal government is prepared to hand out a total of $1.2 billion in loans and grants to coastal states to help them cope with the disclocations and damage expected from production of offshore oil. The amount of aid a state gets is keyed to, among other things, amount of coastol area it has.

If the boundary ends up where Georgia wants it, South Carolina could lose $5 million to $10 million in impact aid, according to knowledgeable sources. And the figure could go much higher if large amounts of oil are discovered.

With exploration by the Interior Department and private oil companies set to begin this summer, the two states have been attempting to work out a settlement. But yesterday a spokesman for South Carolina Gov. James B. Edwards announced that "negotiations have broken down. It seems it will have to go to (the U.S. Supreme) Court."

The dispute began almost two centuries ago, when gold was found in the Savannah River, which forms a natural boundary between the two states.

Officials from both states met in 1787 at the convention of Beaufort in South Carolina and agreed to split the river down the middle.The issue seemed settled, but disagreements have flared up at least three times since the 1700s.

Now, South Carolina claims that a topographical map of the area drawn in 1971 by the U.S. Geological Survey gave Gerogia an area that had been considered part of South Carolina, including three uninhabited islands named Barnwell Island 1 and 2 and Oyster Bed Island.

That new map, which South Carolininas say has no legal standing, gives Georgai a stretch of ocean that veers in front of the South Carolina coast, Georgia claims that it owns the area because several man-made changes in the Savannah River, such as impoundments by the U.S. Army Corps of Engineers, have put those islands in Georgia territory.

If the seaward lateral boundary is drawn 200 miles out to sea from the point that Georgia claims, that state would gain considerable territory at the expense of South Carolina.

South Carolina argues that older maps show the diputed seas - and the continental shelf below belong to it. South Carolina has challenged the validity of maps used by the geological survey to determine the boundary.

While the states negotiate over the big bucks, the dispute has swept up people who earn their livings in the disputed waters. Saxon, for example, has been charged with six misdemeanors in Georgia, including shrimping violations, and obstruction of an officer.

If convicted, the captain could face a $1,000 fine and one year in prison on each of the six counts.

But in order for the case to come to trial, South Carolina would have to allow extradition of Saxon, and there is no indication that the state intends to do so. "It just depends on what the facts are," says Harold Trask Jr., a legal assistant to South Carolina Gov. James B. Edwards. "The captain maintains he never left South Carolina waters. We are still investigating."

South Carolina officials will not admit publicly that extraditing Saxon could weaken their state's position in the boundary dispute, but that view is generally held here. "Technically, the boundary issue will not be considered in an extradition decision," said one South Carolina official who requested anonymity. "But practically, there is no way the boundary will not be considered."

Saxon has hired an attorney and intends to fight the case in court if he is extradited. But he hopes that will not happen. "Georgia is making a test case of this," he tells reporters. "They know if they can win a case over me like that, there won't be a dispute anymore over the boundary."