Sun vs Moon vs Rising Sign
A birth chart is a snapshot of the sky the moment someone was born and is thought to represent the soul's blueprint. While a birth chart is comprised of multiple planets, asteroids, houses and important lines or mathematical data points - most astrologers would agree that the sun, moon, and rising sign are the most influential and important to know.
If you've ever felt like you don't relate to your sun sign, it's probably because you relate more strongly to your moon or rising (also called the ascendant). Let's explore the differences.

Sun
You sun sign is what people mean when they ask "what's your sign?" The sun sign is calculated by figuring out which zodiac constellation (or sign) the sun was in when someone was born. The sun spends roughly one month in each sign.
People often take on certain personality traits based on the zodiac sign the sun was in when they were born. The sun represents our ego and vitality and how our ego relates and deals with the world and challenges. Essentially, the sun is how you show up and shine.
Moon
Your moon sign represents your emotional nature and instinctive awareness. If the sun is how you show up and shine, the moon is how you feel. Your moon sign also sheds light on what you need in order to feel secure in this life.
While the sun is bright, moonlight is dim, and casts shadows on the deeper parts of yourself that not everyone in the world gets to see. This is the you that you hear inside your head whenever you think; your heart, your emotions, your feelings. It is more personal than your sun sign, and since it is our emotional reaction and what we feel, it certainly carries a lot of weight in ones chart. The moon moves quickly, spending roughly 2.5 days in each sign.
Ascendant / Rising Sign
Your rising sign, also known as your ascendant, is the 'mask' you wear to the world and the "you" that you present to the world. It is often viewed as the filter through which one views the world, and the world views them. It deals with sense of self, personality, physical appearance, etc. The rising sign is the cusp of the first house and sets up the zodiac chart as it is the first of the chart's four angles. This point symbolizes the merge of spirit and body, as it the sign that was on the horizon the moment of birth.
Time of birth is required in order to calculate ascendant as it changes every 2 hours.