Nick,
Ahha, this is a difficult question, especially if thought about deeply.
The dictionary says:
Polite- "having or showing behaviour that is respectful and considerate of other people".
Respectful - "feeling or showing deference and respect." / "a feeling of deep admiration for someone or something elicited by their abilities, qualities, or achievements."
So these are the definitions, BUT polite = being respectful. Whenever someone asks 'what is politeness?' we usually say (in linguistics) 'it's respect or showing respect to others'. So in other words to be polite is to be respectful. This is one understanding. They are the same meaning.
Respect can also be 'mandatory'. "respect your elders etc." the problem with the above definition of 'respect' is that is is 'western' in appearance. Many cultures respect others because there are social and hierarchical divisions in their culture. For instance, the way one speaks to older people and younger people. You are not respecting them because you admire their age :) it's cultural. As for 'polite' well this is also cultural. It would take on the meaning: something is polite when it is considered normal, typical in a social interaction based on social rules. An example; you show politeness in some cultures by bowing, if you do not (when you are expected to) it is considered rude. In some cultures showing the sole of your shoe to another is not polite but rude. Finally, it is polite in some cultures to be 'straight to the point' (direct style) and it's rude to be indirect.
This is kind of detailed, so i apologize. I study linguistics and we have studied this question before. You are Chinese? Ask yourself, 'what is considered polite in my home, city, culture?' and 'what is considered rude etc.'
Hope this helps