What's the difference?

No a moisturizer doesnt do the same as a primer. People will add moisturizer to a foundation to get more of a dewey glistening finish. It provides a sheer coverage. A primer is meant to smooth out any imperfections on your face (wrinkles, lines, tiny scarring) so when you apply your makeup it appears to be smoother. Applying a moisturizer is a must before any type of makeup though. If youre going to use a primer just be sure that your skin has had enough time to soak in the moisturizer as you dont want it to thin the primer out.

There is a huge difference. Primer is supposed to be a barrier between your skin and the foundation. In other words, it acts like a lining. Moisturizer, on the other hand, gets absorbed into your skin. If you want your makeup to last on you, you should not use any moisturizer under your makeup. Now, some of the moisturizers contain silicone. If so, the moisturizer, to some degree, could act as a primer but it is not going to be a good one.

A primer helps your makeup stay put longer, I would consider a mattifier as a primer as well.

it depends on your skin type, you can use a mattifier if your skin is oily and prone to shine, however primer can also even the skin tone and take off the extra shine, just be sure to use a high quality brand and not to overdo makeup (you might end looking odd instead of perfect)