There’s no difference in meaning between liter and litre. Liter is the preferred spelling in American English, and litre is preferred in all other main varieties of English.
The word is much less common in American English than elsewhere because Americans generally use U.S. customary units rather than the metric system, which other English-speaking countries use. In American English, liter comes up mostly in reference to beverages (for some reason) and foreign cars.
Outside the U.S.
I bled out two litres of plasma during each treatment, but I was always given back more than two litres of fluid to prevent dehydration. [The Guardian]
The base engine is the new 3.6-litre Pentastar V6. [The Province]
A litre of milk, taken from each ewe every morning and mid-afternoon, is transferred to a refrigerated vat in the factory. [Sydney Morning Herald]
A 2.4-liter, 177-horsepower four-banger claims 30 mpg-plus highway mileage. [Chicago Tribune]
One new event is turkey bowling, which involves rolling frozen turkeys into 10 two-liter bottles. [Buffalo News]