Starter/Fly Wheel Problem

I purchased a '91 Mustang a year ago with a 351 Windsor in it. It ran fine (minus an oil leak) until this spring when I started driving it again. The starter began to spin uselessly. I took it into my uncle's shop and we found out that the starter in it was for an automatic and my Mustang is a 5 speed.

So, we left it in the shop till we could find a new starter for it. Once we located it one for a 5 speed, we bought it and installed it. The car started great for two days. I was getting ready for work and when I went to start my car the spinning sound returned. Which is happening because the teeth of the starter aren't connecting with the teeth on the flywheel; they're just smacking into one another.

Do I have the wrong starter for my flywheel, or is there another problem?

Note: All the teeth on the flywheel are fine.