A name makes all the difference in the fight between Ford and Toyota over who has the top-selling car in the world.

Ford on Wednesday claimed that crown for its Focus compact during the first half of the year, based on registration data gathered by the R.L. Polk & Co. research firm.

The company sold 589,709 Focuses from January through June across the globe, a 20 percent increase over the first half of last year, said Erich Merkle, Ford’s top sales analyst.

The Focus, according to Ford, beat the perennial No. 2 Toyota Corolla, although Merkle said he could not release Polk’s numbers for the Corolla. A Polk spokeswoman confirmed that the number provided by Ford was accurate, but declined further comment.

If the Focus beats Corolla for all of 2013, it would be the second year in a row that Ford lays claim to the top honors.

But Toyota disputes Ford’s leadership. Toyota has said it sold a Corolla hatchback under the Matrix name, and it sells cars that are nearly identical to the Corolla under different names in countries outside the U.S. Ford doesn’t tally Toyota’s other nameplates in its count. Toyota has contended that if all the other nameplates are added in, the Corolla is the winner.

A Toyota spokeswoman said Wednesday that the company disagrees with Ford and is drawing up a response to Ford’s claims.

Merkle said the Focus’ gains are largely due to China, where sales more than doubled to 202,380 in the first half of the year. A new version of the Focus has been on the market only about a year in China, and it’s considered a new product there.

But Focus sales aren’t as hot in the U.S., where they’re up only 1 percent to 188,654 through September. U.S. sales overall are up more than 8 percent for the first three quarters of the year, according to Autodata.

Slow sales of the Focus and the C-Max gas-electric hybrid have caused Ford to plan a two-week shutdown of the Michigan Assembly Plant near Detroit, where both cars are made, during the fourth quarter to control inventory.

Corolla’s U.S. sales also lag the overall market. They’re up 5 percent through September. That’s because Toyota had a 5-year-old model on the market until it was replaced recently by a new, sleeker-looking version.