They had the option to carry on further, they chose not to take it. Ergo, cancelled.
But if the semantics and spin make you feel like Picard won some imaginary war, good on ya! I like both but Discovery will have about 60 episodes by the end, Picard will have 30.
It was planned as a 3 season show and that's what it turned out to be. It may get a spin-off in the form of Star Trek - Legacy, or it may not.
PIC was only going for three seasons due to contracts. DIS only went for five seasons because those seasons were all paid for. There were no concrete plans to continue those shows, even if ideas for a continuation via a Seven or Janeway show for the 25th century, and Starfleet Academy for the 32nd century, were floated.
If they weren't on planning Discovery to last longer, they wouldn't need to reshoot season 5's ending now. Season 5 was not meant to be Discovery's ending, but now it is. So it was cancelled. Not because it's a bad show or anything, but because after 5 season it has become a costly show, with actors to renegotiate new contracts etc.