My experience of learning to canter (in a school) as an adult is that it depends on the horse. And also which lead you want, as most horses have a natural preference for one lead or the other.
Most teachers will ask a beginner to canter from trot at the corner at the end of the short side of the scvhool and the beginning ot the long side. The inside rein may well be slightly shorter to create the bend to go round the two corners. However, if the inside bend is too pronounced in the preparatory trot, the horse will find it difficult or even impossible to canter.
And most RS horses, having transitioned to canter, will go straight down the long side but tend to cut the corners at the far end of the school, as if now cantering a circle. To prevent the horse cutting the corner the student needs to keep a contact on the outside rein to prevent the horse turing in, but without slowing the horse or blocking the canter. You can practise this in walk and trot.
It is easier said than done. One thing that helped me was to be asked to canter the whole way round the school. One doesnt actually have to do this but thinking of the canter as a long distance circuit rather than a short dash down one side of the school helped me to steady the horse.. Horses dont need to go fast to canter and indeed our RI used to teach the walk canter transition, on the straight before progressing to trot canter.