Grass fed typically means they are grazing I pastures, or being fed hay or silage. Grain fed means they are eating corn and stuff from troughs. The reason they are separated is because the fat content and flavor of the beef will be very different between the too. Grass fed beef will be leaner and earthier tasting. Grain fed will be fattier, and less earthy/minerals.

You will also see stuff like Grass fed, grain finished. Where they spend time in pastures, but then spend the last few months eating grains and other stuff. This builds a healthy beef but then cleans out the earthy flavor, which some don't like.