In my mispent youth, I did some work in a body shop and did some body work on a classic 64 Buick.
OK, some of the examples provided in the previous posts are surface rust, others are embedded rust that is permeating the metal, possibly from both sides (eg. probably the Jeep). Wax will temporarily stop or slow down the oxidation process, provided you removed the loose rust and the spot is only surface rust. There are inexpensive auto products that are designed to be painted or 'penned' on and will stop the rust, dead, permanently. I think they sell this stuff in a 'pen' applicator. I used such a product on a 2 year old Buick that someone tried to break into. Seven years later, the rust never returned. Rustoleum, iron oxide red can acheive the same result.
If the frame is rusting from the inside, as auto fenders usually do, you have to invest bucks now or face a broken frame in the near future. That's why cars are repaired by cutting out the rusted metal and replacing it with new sheet metal.
From your pictures, it looks like you have surface rust. The spot on the chain stay looks like the loose rust was not removed. It that is correct, the rust will return quickly. I would try to smooth out those spots with a small piece of fine emory cloth, but don't sand the painted surface since you don't want to repaint, then put some sort of paint or rust inhibitor over it.