Simply, I would say call for is more general and call on is more specific. The teacher called for a volunteer to answer the question. The teacher called on me to answer the question. The goverment called for calm. The government called on the opposition's support. But there are other meanings.

There is no simple answer to your question, because both of these verbs have multiple meanings. There is no clear "difference" here... The best thing is to look in a good dictionary: Cambridge Collins Merriam-Webste,r for sample, and see which of the definitions/ examples correspond to what you think these words mean....