In Memory Alpha, the page on the U.S.S. Defiant states that two Defiant-class ships had that name: the prototype Defiant, and a successor, the U.S.S. Sao Paulo, which was assigned to DS9 and renamed Defiant after the loss of the original. All of this happened during the DS9 series.
In the Star Trek: First Contact movie, the Defiant participates in the opening battle, where a Borg Cube penetrates the Sol system's defenses and besieges Earth. Worf is in command, and is transported out of the crippled Defiant along with whatever's left of his crew by the Enterprise; out-of-universe, this is a rather transparent method to get Worf back into the TNG side of things after the events of ST: Generations, when he moved to DS9 as tactical officer and unofficial envoy to the Klingon Empire.
The question is, was Worf's Defiant in the movie the original, or the Sao Paulo? This would primarily depend on where the movie falls in the overall canon timeline. According to in-movie dialog, whichever one it was was salvageable and therefore would have survived the movie, so the movie would have had little impact on the canon of any running TV series at the time.