I am making a set of 18 inch cabinets to set on the floor behind a bar. My question is do I need to put a toe kick space in the cabinets since they are smaller? What would be the standard?
Its all about comfort and maintenance. If you don't mind the lack of a toe kick then don't install one.
The point of a toe-kick is to give your toes a place to be while working at the counter, if you either won't be working here or it will be minimal, then don't worry about space for your toes, if this is a high traffic area, do not skimp, put the toe-kick in, your back and legs will thank you for it!
Typical toe-kick is 3" - 4" deep and 4"-6" tall, depending on the size and design of the cabinets. Take your cues from other cabinets in the house and duplicate them in this detail.