Spells and Magic

[Thingol]

In the passage where Gandalf is trying to open the doors of Moria from A Journey in the Dark from the Fellowship of the Ring Gandalf says:

I once knew every spell in all the tongues of Elves, Men, and Orcs, that was ever used for such a purpose...

In the letters of Tolkien he specifically states that only Elves can use magic. These two things seem to contradict each other. Answer probably has something to do with differences between lore and magic, but I've always been kind of fuzzy on that. For example the barrow wight blades had spells of the bane of mordor cast on them, but how could men cast spells? I have always been kind of confused about Aragorn's seemingly mystic ability to heal people, but I've always just chalked it up to the teeny bit of elven blood in him.