To be clear, there is no “generation” classification for fighters. This was a marketing gimmick cooked up by defense OEMs to move hardware and keep Congress from axing pet projects. The generation thing appears in the 1990s in Lockheed Martin literature about the F-22, which at the time was in danger of being stillborne. Nobody referred to the ATF program, which sired the F-22, as a fifth generation fighter. It was a fighter program, albeit an advanced one.
Stealth, derived from the old Anglo Saxon word “stealeth” meaning to sneak up upon and overtake by surprise, is a generic term for a wide variety of technologies called Low Observable Technologies. They are intended to reduce the signature of a person, vehicle or structure, by identifying all means by which they can be detected by sensors. This includes visual, infrared, radar, thermal, acoustic, etc. LOT technology then attempts minimize the footprint made. Stealth appears to have been a media thing, similar to how Vespa mandarinia was dubbed ‘Murder Hornet’ - it sounds scary, which gets likes, clicks, airtime and column inches. The origins of the term stealth go back to the 1980s and were most closely attached to leaks about the Have Blue and Senior Trend programs which developed the F-117 attack aircraft. Stealth is also often associated with radar near invisibility and refer to aircraft whose shaping was derived from Pyotr Ufimsev’s research into accurately calculating RCS size. The B-2 “Stealth” bomber program was originally know to the public as the Advanced Technology Bomber (ATB). The term also got traction in Tom Clancy’s book Red Storm Rising, which featured the deployment of a fictional “F-19 Ghostrider stealth fighter” on a future European battlefield against the Soviets.
In short fighters are fighters, stealthy or not.