Training a horse is a process made up of thousands of baby steps, barely perceptible intricacies, and gradual improvement. Layers of training are built into horses over many slow years to allow the horse to mentally and physically adapt. Riding can also be a highly subjective sport. If you had ten different trainers critique a ride, they all would see different nuances. It takes a trained eye to spot these riding faults and a clear understanding of the training scale to know the difference.
Extended gaits are faster than collected gaits.
I’ve seen riders at every level that make the very common mistake of turning onto the diagonal for an extended trot, and the horse merely speeds up in short, choppy strides. Since the speed increases and the length of stride stays the same, the tempo also speeds up.