The "make 1 over" is different from the "Make 1" not only in how you do them, but how they look when you're done.
In a M1o, you simply pick up the thread between 2 sts and work it. This result ends up being like you worked a YO from the previous row which leaves a small but visible hole in your work, giving it a lacy look.
In a M1, you pick up the thread between 2 sts and twist it either left or right before you work it. This action pulls the sts closer together so there is no hole and the new st nestles between the original sts almost invisibly.
Does that make more sense to you?