The neighboring states of Kentucky and West Virginia are engaged in a battle to win what is described as the first big prize in the race to make a usable synthetic fuel from coal.

The fight is a strange one because it doesn't pit Kentucky against West Virginia. Instead, it has made the two coal states allies against the Department of Energy and the Office of Management and Budget, which, after promising a year ago to finance synthetic fuel projects in both stafes, has now decreed that a competition should take place between the states for the best project.

"The way we look at it is there's strength in unity and that's why we're working with each other," said Sen. Wendell H. Ford (D-Ky.), a member of the Senate Energy Committee. "We feel very strongly that two plants are significant and will help in our development of synthetic fuels."

At stake is at least $700 million, the conserveative estimate of the cost to build the nation's first commercial plant to extract from coal a fuel that leaves no ash and does not pollute the air with a lot of sulfur and nitrogen oxides. The plan is to first extract the ash from the coal, thereby making a smaller and lighter fuel that is easier to transport.

There seems little doubt that a synthetic coal plant will win government approval this year. Congress wants one and President Carter apparently wants one, having promised some members of Congress that he will allude to it in his energy speech to the nation on Thursday.

Besides Kentucky and West Virginia, the competitors in the race for the $700 million coal plant are two industrial consortiums headed by Southern Ompany Services Inc. and Gulf Oil Corp. Further, Japan and West Germany are both committed to put up 25 percent of the money for the first plant, though both lean to supporting one approach over the other.

The Southern Company approach is tied to the use of abundant, high-sulfur coal in western Kentucky and involves conversion of the coal into a solid fuel without ash and without sulfur. Gulf's is to start with low-sulfur West Virginia coal and convert it to a liquid fuel.

Pilot plants already have burned both the solid and liquid synthetic fuels. One burned 3,000 tons of the solid, another 4,500 barrels of the liquid. Energy Department spokesmen said the two burns passed "both the heat and the environmental tests."

Each synthetic coal has advantages. The solid fuel will be more free of sulfur and will produce coke as a byproduct to fire stell furnaces. The liquid fuel will be easier to transport and as a by-product will make gasoline, almost an invaluable edge in a day of dwindling oil supplies.

In agreeing last year to back the synthetic coal venture, West Germany came down on the side of the liquid synthetic fuel. West German electric plants burn oil almost exclusively, so if they are to use the end product they want it to be liquid. Also, the West Germans are intrigued by the idea that gasoline will be a by-product of the plant.

Japan is said to feel the same way West Germany does and for the same reasons. If the Japanese are to buy a synthetic fuel, they want one easy to ship from the United States.

Congress may decide to approve both plants, one in Kentucky near Newman across from Evansville, Ind., and the other just north of Morgantown, W. Va. A week ago, the Senate Energy Committee told the Budget Committee it would authorize $59 million this coming fiscal year to start the solid fuel plant and $45 million to begin the liquid fuel plant.

The House energy development subcommittee of the Science Committee recommended $40 million for the solid fuel plant and $50 million to begin the liquid fuel plant.

Around the Energy Department, sources were saying yesterday that it was likely both plants will be approved. There was talk even that President Carter would see the wisdom of such a move and say so in next Thursday's energy address.