Training is important, and I'm sure the feel is different for a horse as well. One of the many mistakes I've made with Mia was trying for contact, but not being quick enough to give her release. My hands were light, in terms of lbs of pressure, but they were not responsive to her. Since she didn't get the release at the right time, even if the pressures involved were small, she would become frustrated and start up with what I now realize are classic bit evasions - everything from nose at chest to rooting. My error, her frustration.
When we switched to curb and using the weight of the rein, she sometimes seemed lost. She stopped well, but it took her a while to realize the reins would stay loose unless I needed something specific from her. If I wanted her to 'collect', I might bump the reins briefly if she tried to root around, but otherwise I would shift my weight back and wait for her to follow...or maybe do some turns to 'force' her weight back.
I'm not saying it is wrong to ride with contact, English style. My screwing it up does not mean others screw it up, and far too many great riders use contact to good effect for me to suggest it is wrong. But the Texas style of western riding kept one hand free to work a rope, and it would be darn tough to ride with contact and one-handed, particularly if you were doing something like cutting cattle, or even moving tough cattle.
So the western approach was to use slack reins, sometimes amplified by leverage. One aspect I've seen but still do not use is from using one hand with split reins. At least when the splits hang down each side, moving the hand also slides the rein against the horse's shoulder. When I do it, Mia responds much faster to the neck rein input, so apparently that feel is its own cue to her. I normally ride with a single loop rein, but eventually will switch to split reins because she responds better with leather split reins.
Western riding is rooted in ranch work and rough country. It is also rooted in the rider having more to do that just ride the horse, so it adapted to a style where the rider pays less attention to the horse and where the horse assumes responsibility for keeping its footing and avoiding gopher holes, cactus, etc.
The guy in the picture owned Trooper's sire and dam, although the breeding was unintentional. Trooper spent his early years as a ranch horse. He didn't work the land in this picture because my friend's lease to run sheep and cattle there expired before Trooper was born - but they still run cattle to the south. To understand western riding, it helps to appreciate what the west can be like. They used to run sheep and cattle thru the bottom land in the canyon:
An English trained horse can learn western, and vice-versa. Riders can learn different styles, too. But it doesn't seem radical to me to say they ARE different, and different for good reason.
I'm trying to adjust to using a western saddle. I primarily rode English and Australian designs. Maybe it is just MY rump, but they sure feel very different to me. If Mia didn't move better in a western saddle, I wouldn't switch. But she does, so I am...and they sure do not feel interchangeable to me! The weight distribution, the loss of feel of her back, the loss of contact between my calves and my horse - it all feels weird to me. But I honestly do not see the point of changing tack if one doesn't also change one's approach to match the capability and history of the tack. I may love a forward seat, but I need to make some big changes in how I ride to get good use out of a western saddle.