Our daughter has difficulty in path planning (fine motor). She was delayed walking and as a result had low muscle tone. Her attention (eye contact, joint attention) was also poor, which made learning other skills difficult. Since very young she would hyper focus on objects like strings and would tantrum when you try to transition her to new task or object. The objects were usually not appropriate or typical and her interaction with them was not considered typical (repetitive behavior).
She now walks, has great eye contact and joint attention and is learning new words everyday (though still has some speech issues). She also plays more creatively and appropriately with toys... it's really opened up so much for her.
Mostly these are play based therapies. The difference is the way that tasks are broken down. For a lot of kids you have to master and work on REALLY basic steps for a long time before moving to even basic things (like stacking rings or requesting an object).
Any kid would benefit from these therapies, there is no magic to them. It's time and observation. We set goals for her then work with specialists to break down the operations and work with her to master fundamentals. Each new skill tends to unlock all sorts of other skills.
ABA is a trial based therapy that has a lot of good and bad information out there about it. It is basically what I just described but in a much more structured and documented manner. It's one of the more researched methods of treatment and has been proven to be highly effective. It's again tailored to the child, so there is no good way of describing other than to say that it emphasizes mastery of skills, errorless learning (no negative responses for wrong behavior) and intense hours (some kids do 40 hours of ABA a week alone).
As I mentioned, each kid really has their own set of issues, so it's tough to say what will work for each kid.
I read a few Behaviorist books when she was diagnosed. A lot of the therapies/techniques are really just good parenting advice.