In any case, the word "cognitive" is used as in "cognitive science",
On the topic of "processing," it's very difficult (sometimes impossible) to know what humans or nonhumans are doing covertly when they "process" stimuli. Thus, I'm not sure how you can determine that "they [animals] categorize differently than us."
A dog that is trained to sit when his owner says, "sit" must be "processing human language" when the dog sits. Right? I know this is an oversimplified example, but I'm just making a point that calling things "cognitive" and referring to "processing" doesn't help explain what is really happening. Sometimes these terms obscure a description/explanation. Skinner [0] makes this point a lot better than me.
[0]: http://carboneclinic.com/portal/conferences/files/IESCUM%20D...