From what I understand, ".22 LR" is nominally .22 inches, actually is .223 inches, and is labeled as 5.6x15mmR in Europe while actually being something like 5.66mm (the 'x15' is the length of the case in millimeters, and the R means rimmed.) They are called different things and both are not quite their nominal sizes, but I think they're interchangeable in practice.