What is spatial correlation and spatial convolution?
These terms exist mainly for historical reasons. In signal processing the signal is a one-dimensional function of time.  So people talk about the time domain vs. the frequency domain.  On the other hand, in image processing you are looking at a 2D function of $x$ and $y$, and there is no notion of time.  Instead your are talking about spatial frequencies.  Hence, spatial correlation and spatial convolution.

Typically, in image processing you simply talk about convolution and correlation.  The term spatial usually shows up when 2-D convolution and correlation are introduced to people with background in signal processing.