ELI5 What is the exhaust from planes?

My brother is convinced that the exhaust from certain planes is a Stratospheric Atmosphere Injection (a sort of geo engineering technique that is currently being tested by the CIA and Bill Gates to help reduce the temperature of the planet). He constantly takes videos of planes over Los Angeles to show how some planes have exhaust and others don’t (which somehow proves his point). He also points to how Tennessee just banned Solar Radiation Management, which he is convinced is a ban on ChemTrails. On the other hand I am convinced this is normal exhaust from a plane. Can you explain what the exhaust from a plane is? Why certain planes have exhaust while others don’t? Why do some planes leave a long exhaust trail while others only have a short exhaust tail that disappears shortly after the plane passes?