Like so many terms these days, CX and touring do mean something but are so broadly, generally, and/or inconsistently used that you can never be quite so sure what they mean. I don't think you can go wrong with either for a commute but if you want to analyze it a bit more then you need to get into the gruesome details.

Every generality (eyelets, frame angles, chainstay length, tires, brake style, etc.) has a basis for its stereotype but there are always exceptions so just make the list of stuff that is important to you and find the bike that has it, rather than starting with a bumper sticker description.