Bleeding sockets need to be differentiated between a true bleeding socket compared with just some blood stained saliva. A fresh bleeding socket will be seen oozing, and not just spitting of blood. It is important to investigate potential causes of the bleeding (is the patient clotting normally? is the patient on any anticoagulants? etc).
Dry sockets usually present with a bad taste, and sometimes also have a bad odour. A diagnosis is often made based on the history, but a tender region, with denuded bone and lots of food debris in the region of a recent extraction are tell-tale signs of a dry socket.
The image below shows a dry socket.
Note how there is denuded bone present in the site of a recent extraction. Food debris is also visible in the area as well.