No. The term "in commerce" is much broader than that. For example, for the purpose of federal registration, the scope is any activity that may be lawfully regulated by Congress under the Commerce Clause of the Constitution. If you are aware of the various things to which the Commerce Clause has been used as a Constitutional basis for lawmaking, then you can appreciate how wide a swath that is.
As usual, there is no one "official definition", but you will find an extensive discussion, limited to the context of "in commerce" for federal registration, here:
http://www.uspto.gov/web/offices/tac/tmep/0900.htm