What are the differences between 依頼【いらい】、需要【じゅよう】、請求【せいきゅう】、注文【ちゅうもん】、要求【ようきゅう】 and 要請【ようせい】?
Some of these words are not even similar to the others, so please learn how to search for the differences. I recommend you use ALC, which is mainly aimed at Japanese people, but has more definitions and much more decent examples. Jisho.org is better at rare Japanese words, but when it comes to understanding common words like these, ALC is almost always more helpful. For example here's the result for 需要.
- 注文: "Order" (for purchasing an item/service; something you make at restaurants or on shopping websites)
- 需要: "Demand" (as opposed to supply; economics term)
- 請求: Mainly, "bill" or "invoice" (i.e., "please pay the money for what we have done"). Less commonly, "claim" (for something one legally deserves, especially in judicial contexts).
- 要請: "Call/request/appeal" officially made for publicly meaningful reasons. Typically a government or a lobbyist makes one.
- 要求: "Claim/request/demand" that may or may not be based on law. Often more demanding, forcible, bold or rude than 依頼.
- 依頼: "Job offer" (if paid) or "(formal but personal) request", "asking a favor" (if unpaid). Usually you can decline it.