As the name implies, Broadway is a wide avenue which runs the length of Manhattan Island, from Bowling Green at the South, to Inwood at the northern tip of the island. It is the oldest north-south main thoroughfare in the city, dating from the first New Amsterdam settlement. The name Broadway is an English translation of the Dutch name, Breede weg. Broadway was originally the Wickquasgeck Trail, carved into the brush land of Manhattan by its North American inhabitants.
The Bowery, as a street, was known as Bowery Lane prior to 1807 and was the road leading to Peter Stuyvesant's farm or bouwerij. Today it runs from Chatham Square in the south to Cooper Square in the north. "The Bowery" is also used to describe a small neighborhood with boundaries at East 4th Street and the East Village to the north, Canal Street and Chinatown to the south, Allen Street and the Lower East Side to the east and Bowery (the street) and Little Italy to the west.
In 1945, Mayor Fiorello La Guardia changed the official name of Sixth Avenue to Avenue of the Americas in an attempt to acknowledge the City's close trading ties with South America and to encourage further commercial relationships. Alas, New Yorkers remained faithful to the old name. After the name change, the street signs carried a unique design and the streetlights were adorned with "Avenue of the Americas" (many of these were removed in 1992, when most streetlights were replaced).
Since New Yorkers seldom use this term, calling the avenue by that name has even become 'a shibboleth' of sorts for something a tourist in the city might say (such as mispronouncing "Houston Street" - should be said as "Howston". However, to avoid confusion among visitors, the street was signed with both names in the 1980's.