What is the betwwen [i,j] and [u,v] in explinations of correlation and convolution (picture attached)?
$[i,j]$ are your spatial coordinates and $[u,v]$ are summation indices. 

The difference between correlation and convolution is simply the sign: correlation has $i+u$ and convolution has $i-u$. 

They are close cousins: it's easy to express one as a function of the other. For example: correlation is the same as convolution with a properly mirrored/flipped version of the kernel. If the kernel is sufficiently symmetric, both correlation and convolution will yield the same result.