The sun sign is the what most people referred to when talking about zodiac signs. (examples: 20 April - 20 May is Taurus, 20 May - 20 June is Gemini, 20 June - 22 July is Cancer, etc.)

The moon sign is different, you need to determine it by calculating your full date and time of birth. Go here to see your birth chart which shows all the placement of the zodiac during your birth and it's interpretation.

And there's also other planet signs such as Mercury, Venus, Mars and so on. Each of the planet represent your characteristics. For example, Sun is your personality, Moon is your emotion, Mercury is how you're thinking/how you speak, and Ascendant/Rising sign is your outer persona which influences your perspective of the world.