The baseline to understanding it is that a player has 10 semesters to play 4 seasons. A redshirt works because it still allows a player who has chosen to forgo a season to complete his or her four seasons in that window. A hardship waiver is for when a player has played in four seasons, but only played in less than 30% of one due to a season-ending injury, and when that player hasn’t completed his or her 10 semester clock.
The new redshirt rules make it more confusing, because a player can play in up to 30% of the season at any point and still redshirt. A hardship waiver still requires the injury to be season-ending, from what I can find.
A player can get a sixth season of eligibility if he or she has missed two seasons due to injury. That and postponing the five-year clock with something like a mission are the only ways to go beyond that window.