The other magic was based off of gemstones. The wizard can summon animals depending on the gemstone used to summon it and the user is able to use the animal in combat. (The animals can turn into weapons as well, again depending on the animal that is summoned.)
I have a lot in mind now. Now I am just agonizing over why these ideas didn't come to me while making the SU. D;
Well one of the ideas is magic that involves photography. So basically, you can take a picture of anything (including magic) and as long as the person who took the picture has the photo he/she can summon it in real life. However, if the person is capturing magic, there is a wait period between 5-10 minutes depending on how powerful the magic he/she is capturing is. See if he/she captured an item, he/she can summon it right away, but with magic he/she will get a blank photo and can't use it until the photo clears up.
I have another one in mind too. (This came while watching the anime Skip Beat. This idea came to me while watching the opening...)