In general "blurring" refers to a wide variety of optical deteriorations of images.

In its more basic form, blurring is intended as convoolution of the image with a kernel that "smooth" the content in the image, by subsituting the intensity of each point  in the true image with the weighted average of the intensities in its neighborhood.

In this form, as the transformation is deterministic.

Partial volume effect refers to the fact that when you acquire a signal from a specific position in space, you are not summing the signal originating from an ideal point, but indeed from a discrete region with a finite extension. Thus, if it happens that within this region there are sources of different signals, you are obtaining a mix of them.

I think the best way to understand draw a histogram of the bullring and non-blurring images.