What is the difference between 人民 and 民族？ 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.