求 (qiú) is a versatile verb covering 'seek, request, beg' — the core idea is actively pursuing something you lack. Compared to 要求 (yāoqiú, a stronger 'demand/require') and 请求 (qǐngqiú, a polite 'request'), 求 is more neutral and can imply a humble or earnest tone, especially in 'beg' contexts. 寻求 (xúnqiú) is more formal and literary for 'seek' (e.g., truth, advice), while 求 is broader and used in everyday speech.