Gelato and ice cream are both frozen custard (milk, eggs, cream, sugar, and flavorings) desserts. They both face the same initial challenge: avoiding crystallization when freezing - i.e. avoiding a grainy custard even after freezing. The differences between gelato and ice cream come from the different approaches to overcoming this challenge. Ice cream is made by constantly and quickly churning the custard as it slowly freezes. Gelato is made by freezing the custard very quickly, under pressure, and with minimal churn. Both processes accomplish the same initial goal, but nonetheless create very different final products.
In addition to a slow freeze, and constant churn, ice cream also uses more cream than milk and relies on a significantly high dairy fat content (typically 14-25%) in order to stay smooth and creamy. Gelato's freezing process allows it to be produced with more milk than cream and a far lower fat content (often 4-9%). Since fats tend to coat the palate and impede the sense of taste, gelato flavors tend to shine through earlier and brighter.
Because gelato is frozen under pressure and with minimal churn, it's far more dense and contains less air. There are some Italian processed gelatos that do have air injected in order to increase the yield. These still have less air than ice cream. Premium gelato contains little to no air. This is why gelato is often described as silkier and more taffy-like.
Since gelato is denser, it stays frozen harder at higher temperatures than ice cream, and is hence often served at warmer temps than ice cream. This also contributes to many flavors shining through very well in gelato since their compounds are better tasted when they and the palate are no so cold.
It may seem like we're making the case here that gelato is better than ice cream. Quite to the contrary, our point is that gelato and ice cream are so significantly distinct that it doesn't really make sense for them to compete. We enjoy them both. Understanding and appreciating the differences allow us to enjoy them more! Life is short. Eat well.