What is the difference between 人民 and 民族, for example in 中华人民 vs. 中华民族?
人民 is translated as "(the) people". You can find it in popular expressions like:
- 人民共和国 = People's Republic; as Huang said in the comments, if we include China it becomes "中华人民共和国"
- 人民币 = Renminbi (the Chinese currency. 币 means "money, coins, currency".)
- 人民日报 = "People's Daily" (a newspaper)
民族 means "ethnic group, nationality", for example:
中央民族大学 Central University for Nationalities
All of the examples have been taken from the CEDICT dictionary.