Augers have a screw tip point and are self feeding. You don't have any control over the feed rate except to slow down the rotational speed. They have sharp edge cutting tip which gives a clean hole, but upon break through they will leave splinters or tearout.
On the other hand, a Forstner also has a sharp pointed tip and sharp edge cutting blade leaving a clean hole, but will not self feed. The feed rate is determined by the amount of downward pressure applied on the drill. Some Forstners have "sawtooth" edge cutters, others are smooth, no teeth, but either will leave a clean hole.
Other choices are twist drills which don't really work well in wood and may wander and leave lots of tearout on break through. A backer board is best when drtilling wood.
Similarly a spade bit is less likely to wander but will also leave tearout, so a backer board is best here too.
Finally, a brad point bit has a sharp pointed tip and sharp edge cutters leaving a clean hole and is accurate. These drills have spiral flutes like a twist drill which carry the waste up and out of the hole as you drill deeper. A backer board will give the best results, but is not always required.
When drilling holes where no backer can be used, expect some tearout on break through, unfortunately.