We have all seen many lists of words that are British English words and their American English synonyms. Some of these simplistic lists include many errors. It is often claimed that parcel is British English and package is American English. Certainly in British post offices the word parcel is used and in American post offices the word package is used. However is this true of the wider use of these words?
Both countries use the word package more often than parcel. England uses package to parcel at the rate of 8 to 1 and America at the rate of 7 to 1. (According to the British National Corpus and the Corpus of Contemporary American English) England uses the supposedly American word slightly more often than the Americans.
Parcel and package are both synonyms for a wrapped box. Package is also used as a metaphor for collections of things sold together, such as computer programs. It is also used in the expression the whole package e.g. all the features of a person, a job, a political party line etc. This use of package is very common in both the UK and US.
The word parcel originally meant a part of something. Parcel can be used to refer to an area of land and this meaning is the original. The word package is constructed from pack and the suffix -age. Both words are about 500 years old and have a long history in England. They are commonly used in both countries, but specifically in the post office one is used more often than the other.
Both of these words are used in both countries, just not always in the local post office. There are too many examples of words wrongly added to British vs. American English lists to print them all here. When in doubt, check a proper dictionary.