let's
Synonym discussion
Sense: idiom/1
All four expressions make suggestions, but they differ in how definite the proposal sounds. Let's is the most direct and assumes the listener is likely to agree — 'let's order pizza' sounds like a decision already forming. Why don't we sounds more tentative and invites negotiation — 'why don't we order pizza?' leaves room for the other person to suggest Thai food instead. Shall we is more formal and polite, common in British English and service settings — 'shall we take our seats?' is a courteous prompt. How about works differently grammatically, taking a gerund or noun phrase — 'how about pizza?' feels like a quick, low-commitment option. Use let's when you are fairly sure the other person will agree; use why don't we or how about when you want to keep the discussion open.
Etymology
Let's is a contraction of let us that first appeared in written English around 1567. The phrase let us originally meant 'allow us (to do something)', but over time it became a conventional way to make a suggestion that includes the speaker and the listener. The contracted form let's emerged in casual speech as the natural shortening of the two words, and by the 17th century it had become the standard way to propose joint action in everyday conversation.