The huge difference between an Initial and Pitch (I&P) and a VRIAB is that the I&P is a level turn from circuit height, normally 1,000 feet, whereas a VRIAB is a climbing turn from whatever lower height you can get away with.
A lesser difference is that for a VRIB the downwind leg must be clear of other traffic. For an I&P you can have other circuit traffic, in which case you must continue upwind until you have visually accounted for all the other traffic before pitching onto the downwind leg.
The RAF JP schools would only allow 4 jets in the visual circuit at the same time. Not so " "Ronny RAAF." One night, I called at Inititial to join the circuit at RAAF Pearce. "Clear to join, ten in" was the reply from ATC. By the time I had counted all ten ahead of me, I was getting close to the boundary of Perth International.
Halcyon days!