To me, there is only one really effective form of pressure, and that is mental pressure. Mental pressure happens when your horse is thinking "The human wants something again, I really need to figure out what it is." This state of mind can happen in a variety of ways, like if a horse is wanting a treat and is looking for a way to get the human to fork it over.
More common though, is when the horse is uncomfortable and is trying to find the way to get comfort again. Making a horse uncomfortable is pretty easy to do. As I have said before, even staring at a horse too hard can create the mental pressure needed to get a response. Unless you are really good at thought transference, or are telepathic, training your horse will require more than just staring at them and thinking about what you want them to do. Some amount of physical pressure is needed. Physical pressure is definitely not a bad thing, it helps a horse take the guess work out of trying to figure out what you want, which actually relieves a lot of mental pressure and stress in the long run. Physical pressure comes in two basic forms: rhythmic pressure or steady pressure.
Steady pressure is when you push or pull on your horse with an even uninterrupted feel, it works best in close quarters with your horse, think leg and rein cues while riding or asking your horse to drop its head for bridling or grooming. Rhythmic pressure when you tap your horse,wave your arms, swing a rope, or slap the ground, anything that creates constantly intermittent source of discomfort for your horse. It is much harder for a horse to push against than steady pressure. Imagine pushing on the blade of a fan while the fan is turned off, that is steady pressure, it is easy to push on. But when the fan is turned on, contact with the blade would be constantly intermittent, or rhythmic pressure, trying to push on the blade of a rotating fan is a lot more uncomfortable, and I'm pretty sure if you try it, you will quit rather quickly. Rhythmic pressure is much more adaptable to a wider range of circumstances.
In my experience, steady pressure seems to be harder for horses to understand. When working with mustangs, the first time they feel even an extremely gentle pull on them through a rope or halter, they regard it as a crisis situation, all of their instincts push against the steady pressure and it takes a great deal of conditioning for them to stop fighting and begin to yield to the pressure. With domestic horses a different problem arises. The domestic horse gets so used to being pushed and pulled with steady pressure that they can get very dulled. Often when a horse becomes dulled to steady pressure, it is rhythmic pressure is what is used to lighten the response again. An example of this is a rider who has a horse that does not move well off the steady pressure of leg cues can use the rhythmic pressure of a riding crop to reinforce the leg cue. This same principle can be used any time a horse gets dulled to steady pressure, on the ground or riding.
Rhythmic pressure seems to be more natural for a horse to understand. Yielding to rhythmic pressure is one of the most important things for a horse to understand to keep a handler safe on the ground. When a horse is behaving in a dangerous manner, either out of fear or disrespect, they need to be driven far enough out of the handler's personal space that the horse can't make contact with teeth or hooves(this implies using a lead rope long enough to achieve this distance). You cannot push a horse out of your space far enough using steady pressure.
The greatest difficulty most people and horses have with rhythmic pressure is not being clear in the difference between rhythmic pressure and rhythmic motion. Rhythmic motion is used to build a horse's confidence, like repeatedly stroking a young horse with a saddle blanket, or waving flags around to teach horses to be calmer around moving objects. To be really detailed about the difference between rhythmic pressure and motion I would have to write another whole article, for now this rule will have to suffice: If your rhythm is intended to cause your horse to do something, that is rhythmic pressure. If your rhythm is intended to cause your horse to be calmer, that is rhythmic motion.
Then the question arises, which type of pressure is best to use for certain tasks? That is another complex subject, but really it comes down to what will work for each individual horse in a given circumstance. I think it is important to be able to use either type of pressure for most tasks. To give a couple examples; my horse moves laterally off of leg cues when I am riding or when on the ground I can put a rope around his girth and pull him towards me, but I can also wiggle my finger at the same spot on his body and have him yield laterally. The rope and leg are steady, the wiggling finger is rhythmic. Normally leading my horse forward only requires a steady drawing pressure, but if I want more speed I will reinforce the draw by slapping the ground with my stick'n'string.Both are absolutely vital for your horse to understand and respond confidently to. It is often necessary to use both at the same time to reinforce, or to teach.