PVA Glue is the category that includes standard white glue and yellow glue. It is the most common glue used by woodworkers. (Yellow glue is also called carpenters glue.) Unless you are working with materials that will be constantly exposed to water, PVA is the glue you probably will use over 95% of the time. It is inexpensive (compared to other glues), non-toxic, and has a long shelf life.
The glue solvent is water and works by intertwining the fibers of wood with the polyvinyl acetate as the water evaporates. The bond strength of PVA glue becomes stronger than the wood itself, so bond strength between white and yellow glue makes no difference.
The basic difference between white glue and yellow glue is that yellow glue has a shorter drying time (open time), usually about five to ten minutes. Another obvious difference is the color. White glue will dry clear and yellow glue will keep its yellow tinge after it has dried. The color difference should not matter to most woodworkers because the dried glue should not be visible on a finished piece of furniture. Gluemakers however have made dyed PVA glues that will dry a darker color to match a darker colored wood.
Its only real drawback, being a water based glue, is that it is not very resistant when exposed to high moisture levels. There are new PVA glues on the market that are more water resistant than the standard white glue. These glues will be labelled 'water resistant' or 'water proof ' but in this case it might be best to read into other glues that might be better suited for your application.
Another reason to maybe think about not using PVA glue is the fact that the high water content in the glue may not work well with certain types of wood that either warp easily (ie. beech), or are oily (teak).
Do no let PVA glue freeze. It will not be good afterwards. With white glue, if the glue has frozen and then thawed, it will dry a white cloudy color instead of clear. If you are not sure if your glue has been previously frozen, test it first. If it dries white instead of clear, then discard the glue as the bond it creates will not be strong.
Some woodworkers prefer to work with either white or yellow glue. Myself, I take the white glue because it gives me an extra 5 minutes of open time to set up my clamps properly.