Why they are secret
Neither ending appears on the original 12-ending list. They were added in a later Early Access update, and the game does not advertise them in the normal route flow. You find them by doing something the tutorial never suggests.
Off Air: take no photos
The Off Air ending requires a full run without a single photo. The park asks where the news is, the station complains, and the screen eventually cuts to color bars. The people start talking to each other, and the ending card appears.
This is the only route where the correct action is inaction. It is also the shortest secret to attempt, at about a minute.
Star: catch the scream
The Star ending depends on one frame. A spiky-haired square screams at a passerby, and you have to photograph the scream while it is happening. Miss it and the broadcast tells you that you just missed it.
Hit it and the station turns the screamer into a celebrity: local nobody goes viral, the park loves them, a star is born, and the star show begins. The ending is a sharp little parable about fame.
How to practice both
Off Air needs discipline, not skill. Start a run and keep your hands off the shutter. Star needs timing, so watch the spiky-haired square and wait for the scream instead of photographing the wrong frame.
Both endings are tracked in the endings menu as 13 of 14 and 14 of 14. If the card number says 12, you are on an older build or a normal route.