There was a linguistic shift that happened and what the term Roguelike means changed dramatically. Roguelike used to refer to a game based pretty closely on Rogue: procedurally generated dungeons, perma-death, item identification, a hunger mechanic, a specific implementation of turn based combat. Even ASCII graphics were considered necessary for some people. There was an organization formed to police the boundaries of what constituted a Roguelike that was, for better or worse, like the Académie Française in its pedantry.
In Japan, Roguelikes never went out of style in the same way because traditional dungeon crawlers kept being made. So Roguelike elements found there way into games as diverse as Azure Dreams and Baroque.
It took longer for American devs to realize that the basic joys of a Roguelike: the novelty of procedurally generated content, the pressure of permadeath, and the risk/reward tradeoff of trying to go down one more floor. Once indie devs caught the Roguelike bug, it became an epidemic of inserting elements of a Roguelike into every genre imaginable. This new genre was deemed the Roguelite, though this didn't make the Rogue purists happy as they had a much more restrictive definition. And some people just call them all Roguelikes.
Personally, I love both Roguelikes and Roguelites, whatever you want to call them. Slay the Spire is one of the greatest video games ever made, and that wouldn't exist without Rogue, even though on the surface it shares very little in common with its ancestor. Under the surface you find the same joys: risk/reward, high difficulty, just one more run.