Any unauthorized use by another of the same or a confusingly similar mark for the same or closely related goods or services would constitute trademark infringement. The test for infringement is whether, because of the similarity in the marks as well as in the goods or services of the parties involved, consumers would be likely to mistakenly believe that unrelated parties are in some manner related or associated such that the goods or services share a common source.
The clearest infringement is a case of unqualified "piracy." If Clandestine, Inc. manufactures and sells T-shirts with Disney characters and Disney logos on them, the public will likely think they were manufactured, licensed by, or originated from Mickey Mouse and the people at Disney.
A more difficult case of trademark infringement is the one brought by a company called DREAMWERKS against the well-known moviemaker DREAMWORKS. The plaintiff organized science fiction conventions for "Trekkies" and like-minded individuals. The names were similar and the goods and services were somewhat related, but, if anything, it presented a case of possible "reverse confusion." That is, the later-used DREAMWORKS was more famous than the earlier-used DREAMWERKS, and therefore people buying tickets to their conventions might think that the organizers were related to the big, well-known moviemakers. The moviemakers filed a motion to have the case thrown out, but the court said the issue was close enough that it should go to trial.