Whilst I agree that a synonym can be "a word having the same or nearly the same meaning as another in the language", I don't believe you can use that argument here.
Americans never use the word "nappy" to mean something to catch baby poo. We never use the word "daiper". So therefore although they are technically synonyms for each other, they form no practical usage whatsoever when comparing British and US English.
You would have been better citing the example of "sidewalk" and "pavement". To an American, the pavement is a road surface, not an area to the side for walking on.British people do not use the word "sidewalk" and so in British English they are not really synonyms. In America they have distinct meanings and are therefore not synonyms.
Mr Anal (synonym for pedantic git).