Here in America, we get both Accords, too. But under different names.
The smaller Accord Euro is sold here as the Acura TSX. Honda's posh Acura brand optimistically pitches the TSX as a 3-Series rival.
The big Accord is actually the super-sized US market Honda Accord. Acura also sells a fancy version of the bloated US-Accord as the Acura TL, which has been recently rechristened as the TLX
Oh, and we also had the Legend, too. But it's called the Acura RL over here. Acura has just launched the new redesigned model as the Acura RLX.
You can use this handy chart to understand how Honda's Acura division models stack up......
US-spec Honda Civic saloon = Acura ILX (Formerly the Acura CSX in Canada and known as the Acura EL in Canada prior to that)
Global Accord (AKA Accord Euro) = Acura TSX
Fat-Pig US-spec Honda Accord = Acura TLX (Formerly the Acura TL)
Honda Legend = Acura RLX (formerly the Acura RL)
In previous years, Acura also offered an Accord-based coupe (Acura CL) and the older Legend, Integra and NSX were also sold here under the Acura badge.