Let us go. (= Allow us to go.)
Let's go. (= Shall we go?; Why don't we go?)
***** NOT A TEACHER *****Hello,
May I add my two bits to the teacher's excellent answer?
1. "Let us go" is like a demand or order. A bad man has locked you and a friend inside the room. So you yell, "Let us go!"
The subject of the sentence is "you." In other words, "You let us go!"
a. This is
never contracted.
2. "Let's go" is a suggestion that you say to yourself and the other person(s).
a. The subject is "we."
i. In much older English, we would express this idea something like this:
"It's very hot today.
Go we to the beach."
b.
Usually, we always use the contraction.
i. But in very
formal situations, it sounds more dignified NOT to use the contraction:
(a) "Let us pray" (instead of "Let's pray").
*****
P.S. Yes, I believe that it
would be possible to say "It's hot today. Let us go to the beach" instead of "let's go to the beach."
It depends on how you pronounce "let." If you pronounce it gently, then it is a suggestion. But if you pronounce it very
strongly, then it is a demand or order. Your mother has just told you and your brother that you two may not go to the
beach. You yell: "
MOTHER! [You]
LET us go to the beach!"
*****
In order to avoid confusion, many teachers suggest this "rule":
a. When you want to make a suggestion, almost always use "let's." (Except in
super dignified circumstances.)
b. When you have a demand or order, always use "let us." (That is,
you let us.)
James