A full atx board will usually use all the standoffs. Yes, the standoffs are the brass hex shaped barrel nuts. They have male threads on one end and screw into the back panel behind the motherboard. The other end has female threads and it's what you screw the motherboard retaining screws into. If they came preinstalled though in an atx configuration and say you installed a micro atx motherboard there would be a couple extras that you could go ahead and remove. You'd see them because they'd be exposed.
It's a good idea to remove any extras since those barrel nuts act as a ground to the case chassis and you don't really want extra protrusions that could potentially make contact with something else like a misc wire, extra molex or something and create a direct short.