求める | Demand OR ask for, also to seek. (Chinese students were seeking democracy). $$$ |
要求 | Demand – more strident than 求める; you wouldn’t use it to mean ‘to ask or seek.’ $$$ |
需要 | A technical, economic word. Supply and demand. Increasing demand for petroleum. |
請求 | Demand for money – usually used only on invoices and bills. |
欲求 | Personal needs (love, shelter, food). |