Yes, you are correct, but as you move up the levels a change rein is not always going to be across the diagonal. If you follow the letters in the test, this will tell you where to go, if it say HXF then ride through the corner on the left rein to M, tun onto the diagonal and ride a straight line through X to F and then go on the right rein through the corner.
The terms left and right rein are in trot as the left and right leads are in canter, it only tells you what direction you are going, and doesn't give any indication as to a rein you are engaging or pulling on. Throughout the entire dressage test you want your horse moving forward from both legs into both reins evenly. What a judge would be looking for in this level is an accurately ridden pattern, with a rider in good control of her horse and sitting properly and a horse moving rhythmically forward and being relaxed while only accepting the contact. The horse does not necessarily need to be round or in a frame, it just needs to be accepting the bit, and not tossing it's head.