The difference in intention is a major factor in what sets our arts apart.
Within the Yizong school we train Hebei Xingyiquan, Gao Style Baguazhang and Chen Pan Ling Tajiquan. The differences in intention can be seen in how the arts of Xingyi, Bagua and Taiji are applied. This is not something that you can necessarily see all that well when someone is doing a form, but may be obvious when one is applying their intent towards another person. I would also say that it is very difficult to feel the proper intent in your forms until you have a proper understanding of how it is being applied with resistance. This is why it is so important to train both solo and two person practice. If you do not train both then there is a likelihood that you are missing a piece of the whole.
The majority of my experience in this matter comes from training the Hebei Xingyiquan and Gao Style Baguazhang of the Yizong system taught by Luo Dexiu.
The intent of Xingy is such that it overwhelms an opponent with force. Xingyi is much like a tank; it rolls right through obstacles and simply blasts things that come up against it. Xingyi is well suited for people with a large frame. This could be why it worked so well for masters like Hong Yi Xiang and why he was renown for his tremendous power and skill.
Just a few more ideas about training intent...
Intent at different levels of intensity:
I can apply my intent at different levels of intensity when training both solo and with a partner. My intent does not have to just blast on. It functions more like the dimmer switch on some lights. I can play my intent light, keeping the level of intensity low so as I do not alert someone to my intentions. I can play in the mid range, clear and in control. I can play my intention at full intensity, overwhelming my opponent with the force of my mind and body.
Use a training partner to develop my intent.
By training with a partner I can see where the proper use of different levels of intention can help me to effectively engage and eliminate my opponent.
Remembering how your body and mind felt when you engaged your partner and plugging that into your solo practice is the next step. Forms help to develop focus. If you know what to focus on and how to do it then this type of training can have great benefit.