The "minus" means "this size, and all the sizes below it." So 1/2" minus is 1/2" stone with everything smaller down to sand and dust. 3/4" minus has 3/4, 1/2, etc. If you ordered straight 3/4" stone, you'd get just that without all the smaller sizes. For some uses, the fines are used to help lock in the larger stone, like in concrete and driveways. For other uses you don't want them so you can keep the water channels open (rip-rap, drain layers in roads or septic, etc.) or if you are tightly controlling your proportions of a mix.
Other terms we see in our area are "pit run" (nothing run through the crusher/grader, so it can include both broken and rounded stone, often softball size and larger); "crusher run" where you get all the sizes straight out of the crusher without grading, starting at whatever the largest size through the crusher is, even up to 5 or 6" sometimes; and "crusher fines", which are coarse sand-size bits of broken rock out of the crusher, not rounded like beach or glacial sand.
Different pits will give you different products, where I grew up the pit was glacial till, so have a lot of rounded rocks and boulders, all mixed of various types of granite, sandstone, and others. Where I live now the pit is a granite hill where they blast off a "face" and run it through the crusher, so it is all granite unless you specifically ask for river stone which they truck in. Other places in the country your local pit may be limestone or sandstone or something else. In NY I would expect a lot of granite like here...?
Odd tidbit of information: Don't count on crusher fines keeping the weeds down unless it is in a heavy vehicle traffic area to stay tightly packed. Breaking up the stone exposes a lot of nutrients that plants and weeds seem to crave, as well as holding water between the jagged surfaces.
