Flights to the US use the piece cocept for luggage. Flights to other countries use a weight concept. I think this rule is written somewhere in the IATA rules.

For example. On a flight with LH in economy to the US you can check in two suit cases each I think 22kg (44lbs). I remember when the limit was 32kg (64lbs) per item. Flying LH in economy to Asia you are only allowed (40lbs). Which you can put in one suitcase or two if you like.