auxiliary verb
indicates will; intention; let's
Expresses the speaker's volition or intention. When used with the volitional form of a verb, it can also function as a cohortative ('let's do something').
私がやろう。
I'll do it.
一緒に映画を見よう。
Let's watch a movie together.
auxiliary verb
indicates invitation; shall we?; why don't we?
Used to gently invite or suggest an action to the listener. Often softened with か (e.g., 行こうか).
そろそろ出かけようか。
Shall we head out soon?
お茶でも飲もう。
Why don't we have some tea?