That makes sense; I don't actually know much about this.
That being said, weirdly, the normalization by standard deviation happens outside the call to `cov` in the paper (page 181, column 1, equations (unnumbered) 1 and 2). And in equation 2 they've expanded `cov` to be the sum of pointwise multiplication of the (scores - average score) people have given to posts.
Again, not my area of expertise, just looking at the math here.
Yes, they are basically the same thing, but for correlation the values are first zero-centred.