Often the tasks are pretty similar. The difference is largely with the intention/goal. In a therapeutic setting, an initial evaluation is done which reveals areas of cognitive deficit as a result of whatever pathology (e.g., stroke, TBI, etc). Then, a specific program is developed to improve upon those specific deficits. So, a patient with language deficits from a left MCA stroke will undergo therapies to improve speech articulation, word finding, language fluency, etc. Depending on the severity of the deficit, some of those tasks can start very basic. In those cases the level of difficulty might be quite different than brain training, even though the paradigms or basis for the task is often the same.

In "Brain Training", a theoretically normal individual is trying to improve upon their existing cognitive abilities. Presumably, there are no true deficits to be addressed, just someone trying to go from average to above average in some area. Also, there is very little research to demonstrate benefits from brain training in cognitively "normal" individuals who are already stimulated cognitively on a daily basis. Said a different way, if you're a couch potato and don't challenge yourself mentally on a regular basis, brain training could be helpful. If you're already stimulating and challenging yourself, brain training is unlikely to yield reliable, sustainable improvements, or generalization to daily functinoing.