From experience, when Lubavitchers say “Chasidim,” they’re mainly talking about Chabad or, at the very least, including themselves in the greater Chassidishe world.
Most people probably aren’t talking about Lubavitchers when they say chassidim. Lubavitcher’s use pronunciation like Litvaks, they hold by the Gra’s times, they don’t dress like other Chassidim, they don’t seem to get married as early at other Chassidim, etc.