'How do you do?' 'How are you doing?' What's the difference？
Note the corrections I've made to your question.
The answer to your question is this - they are very different indeed.
1. 'How do you do?'
This is a rather outdated and formal expression meaning 'It's a pleasure to meet you'. A conversation might go like this:
A: Bill, this is my colleague, Charles.
B (to C): How do you do?
C ( to B): How do you do?
This would probably be accompanied by a handshake between B and C. As you can see, 'How do you do?' is not a genuine question, because the response is to repeat 'How do you do?'. You would only use this on the first occasion you meet someone, and only in a formal context.
2. 'How are you doing?' is a question, and it's an informal variant on 'How are you?'. For example:
A: Hi. How are you doing?
B: Great. How are you doing?
A: Not bad.