Spell Cards are more than just extra patterns, kind of. They're usually more beautiful and complex than noncards, they're given a name and a cut-in appears. You also get a Spell Card bonus if you capture the card (no deaths or bombs) and a bonus for how many bullets were in play when you beat it. Some also give you a few items. It's also usually a counter for how far you are in a battle.
Going past the games, in Touhou these flesh out the character a bit, giving a demonstration of their ability or style. You have a specific amount of cards to use and once you're out of cards you formally lose the fight.