A vivid dream is so detailed and clear it feels as though it could almost be a memory of something that actually occurred.
A lucid dream is a dream in which the dreamer is aware they are dreaming but continue to dream. It is almost like waking up within your dream. Some dreamers may be able to have a certain degree of control of their dreams while lucid dreaming. The dreamer may choose to explore something, face something, or stop doing something and move onto something else when lucid dreaming for example.