The higher rarity your card is, the stronger the card is from the beginning:

Grey = Common
Blue = Rare
Purple = Epic
Gold = Legendary

Higher rarity also means the card have more room to level up. Common card can only level up to 10 but Legendary card is up to 40. For reaching every 10 levels your card will get an extra star. So potentially a Legendary card can go up to 4 stars.