For example is there a difference between "let the people sing" and "let people sing"? I think in the first case it's like "Allow the people singing" and in the second is like "If you can't sing, people could sing for you". Is that correct? Thanks...
Let the people sing vs let people sing
If you are referring to all persons in general, you say "Let people sing". Another example: People were dancing in the street.
On the other hand, if you are referring to a particular group of persons, you say "Let the people (for example, present in the hall) sing.