The difference lies in the work each requires. Sanding means that the polyurethane finish and some of the damaged wood needs to be sanded down and removed, while buffing just require the removal of the finish. If the scratches don't reach the wood beneath the finish, all you need to do in this case is to use a buffer on them and then apply a couple coats of finish to have them looking as good as new in no time at all. Needless to say, this would be ideal because buffing is significantly easier, less time consuming, and less expensive than sanding them down to the wood. Nevertheless, both practices follow the same steps.
The first thing you need to do is rent the proper tools, which can often be found at most tile stores and hardware centres. Depending on the extent of damages you'll want either a buffer or an orbital sander. You’ll also want a high-quality vacuum that can clean up all of the dust that there will be left when you're done. After the floor is evened out you will need a finish to put on the wood to protect it. The water based polyurethane is a good option. It takes three hours to dry and might require a second coat. The finish should be reapplied every few years for continued maintenance, or when the floor begins to look worn. Oil based finishes are also available for a lower price, but take longer to dry.
Once you have all of your equipment the room needs to be cleared of furniture for the work to be completed. Then clean the floor with either specialty wood cleaning products, or a homemade mixture of one part vinegar to ten parts water. Dry the floor after with with a towel or soft mop.
Begin the sanding the floor along the perimeter and corners of the room with a power hand sander loaded with 30-40 grit sandpaper. Four to six inches from the baseboard is typically fine.
The Main Event
At this point, if buffering, attach a buffing pad to the bottom of the buffer and be sure to use a dust mask to shield from the powder it will create. Begin the process at the side of the room furthest from the door. Move the buffer along the grain, overlapping each lap by a few inches. It’ll be easy to keep track of what you've done by the dust created. Keep the machine running the entire time but stop occasionally to clean the pad. Be sure to buff the whole floor and not just the scratches to ensure that it will be even when you're done.
Follow the same steps if you are sanding them down more extensively with the orbital sander. You will do this over the course of three session with gradually lighter grit sandpaper. Begin with a coarse 30-40 grit, then a medium 50-60 grit, and finally a fine 80-100 grit. If the floor is rough after this, gently buff until it is smooth.
Let the dust settle for a little bit before bringing the vacuum and broom in to sweep up. Clean with the flow of the boards at first, then across them to get everyone you missed. Finish by using a micro fibre cloth to collect remaining particles.
Refinishing the Floors
Staining the wood is only necessary if you want to alter the colour of the wood. To do this apply it evenly along the edges of the floor are then use a roller to spread it evenly on the floor until achieving the desired depth of hue. Once it is dried, then apply the polyurethane in the same manner. Go with the grain and overlap each pass slightly. Continue like this until the floor is covered, and wait three more hours before recoating. Wait a couple days before moving the furniture back in.