How is a U.S. company's international marketing different from or similar to that of its marketing within the United States?

Your professor may be looking for a specific textbook
answer we are not privy to, but I can help you with the fundamental differences and
similarities.

Differences: 

1) 
Cultural differences - most foreigners do not watch as much television as we do, and
they tend to read more, so the approach you take with marketing has to fucntion in a
different media model. 

2) Language - of course, marketing
fluent in the local languages is a must, and sometimes in multiple languages.  Nuance
matters, as does subtlety.  What is unoffensive and humorous in our language sometimes
translates into something completely different.  There was the famous Chevrolet disaster
of marketing the Chevy Nova in Mexico - "No va" meaning, it doesn't go in
Spanish.

3)  Buying habits - Many people in foreign
countries do not have refrigeration as it is very expensive, so they tend to shop every
day, and buy smaller quantities.  Costco-Europe, for example would have a hard time
being successful, as people just don't shop in huge quantities like that.  In many other
countries, there isn't the buying power in terms of economic strength to do
so.

Similarities:

1) 
Materialism is nearly universal - what motivates buyers in the US often motivates humans
everywhere - to find a convenience, to rest and recreate, to be fashionable and
popular.  So the underlying motivations for the individual economic behavior of a human
is the same almost anywhere.

2)  Price consciousness - All
humans, not just Americans, want to get the best deal possible.  They often react to
sales and sales prices in the same manner - by buying more.  Marketing has to be
adjusted to reach the audience, but many of the basic tenets are the
same.

3)  Demographics - I think you'd find that marketing
techniques that are successful in the states with the under 18 demographic are
successful in many places, and the same could be said of the senior citizen
demographic.  Cultural differences exist, to be sure, but marketing toys to young kids
and medicine to senior citizens is bound to find some success in any
market.