A visual circuit is flown visually by the pilot in very close proximity to the airfield normally at 1000ft. The pilot is responsible for separating themselves from other aircraft and then reporting to the controller at 2 points.
The pilot reports when he is downwind. At this point they also include what type of approach is planned on being carried out (L/TG/LA) to aid the controllers planning. You should in response be told how many aircraft will be making an approach to the runway ahead if you and the surface wind. The pilot reports "finals gear down". This is made just as you start your final turn towards the runway and in response you will be given a clearance.
In reality military aircraft cut out the crosswind and base leg. Instead both are 180 degree turns on to reciprocal headings.
A radar circuit is much wider and is vectored by a controller out to about 10nm to allow the pilot to fly an instrument approach like and ILS. The positions in the circuit are the same but is entirely vectored by the controller and normally flown at about 2000/1500ft depending on the terrain around the airfield.