As far as I understand, process characteristics are properties taken from the machine where the finished good was produced, example: speed, pressure, temperature, reaction times, etc. and PRODUCT characteristics are properties or indicators related to the product or material, such as: dimensions, viscosity, hardness, weight, etc.
Normally the product KC's will be "tied" or linked to some of the process KC. If you do not control your process you would face problems with your product.
Hope to be helpful: