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.