Pullups (or pull-ups) are an exercise similar to chin-ups. The difference is in the grip: pull-ups are done with overhand grip (palms facing outwards) while chin-ups are done with underhand grip (palms facing inwards).
There is a third alternative to those exercises: a neutral grip (palms facing each other) that is our favorite (best position for wrist, elbow and shoulder joints).
The classical pull-ups are stressing more lats and somewhat less biceps. The reason is that the overhand grip puts the biceps in less favorable position (you know the difference between biceps curls and overhand biceps curls – overhand curls are much harder) and therefore slightly more work is done by lats.
The difference is not huge: if you take two athletes and let one of them do chin-ups and the other one pull-ups for a period of time, you will probably not see any difference in their muscular development.
It is always beneficial to train the muscles from various angles and this is why almost all coaches advise changing the grip from time to time.
The torso should lean backwards in an angle of about 30 degrees. At the end of the contraction you should squeeze the shoulder blades together (scapular retraction).
For additional resistance do weighted pull-ups with a dip belt that allows adding weighted plates.