I wonder if there is subtle difference between "1" and "2".
For example, 1 is more polite?
1. May I help you?
2. Let me help you.
Hi wow. There is a subtle difference.
"May I help you?" is a polite offer of help to somebody who might be even be a stranger. You are showing your willingness to help but it gives them the opportunity to politely refuse by saying something like, "No thank you, I can manage it OK". It is also a common way for a shop assistant to approach a customer.
"Let me help you" is a little more direct and informal, you might even start helping the person as you say it. If a friend, for example, is getting a large box down from a shelf you might take one side of the box while saying "Let me help you with that".