Correct number of teeth for the metal thickness is important to speed. Bigger teeth let you go faster... but too big and it becomes difficult to saw at all. A smaller/finer blade than you need will feel smooth and be easy to control, but will take longer.
What's different between what you're doing and the videos you're watching? If they are stroking faster than you, that's just experience and time and moving faster. If they are stroking the same speed as you, then each stroke is cutting farther - this could be that your blade is smaller than theirs, or you aren't using the full length of the blade to cut.
But - I think the main thing is practice. Everything is slower when you're new, and going slow is good - it lets you focus on accuracy and good form. Hold the saw lightly, keep the blade going straight up and down, and be careful to stay on the line. Don't push or force the blade along the cut. You'll get faster in time.