Here is my thought, How can I help you ? - a process / steps that will be taken to help out. Example - explaining a math problem. Providing some type of service. Ex. How can I help you ? Yes, can you help me find a sweater? What can I help you WITH ? I see this as providing a helpful hand in helping. What can I help you with ? Please take these bags from me. I see your point. They are "the same" but I think the environment or the situation change their meaning a little bit.

1. The question "What can I help you?" is not grammatically correct. the question should be: What can I do for you? 2. The question "How can I help you?" is correct. Your observation is correct for your level.