So I don't normally correct people, but canter leads can be pretty confusing. The first beat is actually the outside hind leg. That is the leg all horses start the canter on. That's why we ask for the canter with our outside leg. The next beat consists of the diagonal pair. So the inside hind and the outside front. The last beat of the canter is the inside front, which is the lead, which stretches forward farther than the outside front. (source- I'm a riding instructor and a degree in horses)
Yes its really hard to explain over the computer, but you are correct. In my mind i order the beats in level of what i pay attention to the most, i make sure to check my lead and then the hind end so thats why i refer to the lea as the first beat. But thank you for clarifying!