To ride properly, I.e.; quietly, with soft hands, a good seat, and using the correct leg and seat cues, requires finesse.
You cannot acquire the proper finesse without a professional trainer who is skilled in bringing along young or green riders. If you've never had a lesson I consider you a green rider no matter how well you think you ride.
The tack is not the only thing that makes each discipline different. There are cues and ways of riding that cannot be self taught, especially the more subtle things.
Anyone can buy English or Western tack and plop it on their horses, climb aboard, and hang on. That does not make one an accomplished rider by any stretch of the imagination.
The people who tell me they're self taught don't need to do so, because I can see it in the way they ride their horse. Ham fisted, legs swinging, arms flapping like a chicken, and balancing off the reins.
Anyone who wants to make sure their animal is enjoying the ride too, gets the proper training. After all, everything we do should be for their comfort, not ours. They're the ones hauling our butts around, so the right training is necessary to make sure they're not being abused, however unintentionally.