Desk and table lamps may at first seem to be the same thing but there is most definitely a slight difference in these two items as regards their functionality.
Table lamps might be seen as the more decorative type of lamp, perhaps used for some armchair reading but typically just to add more light to a room. In the case of Tiffany style table lamps, it is easy to see how these types of lamps can also be used as a decorative piece by day.
Desk lamps on the other hand have a more definite function as they are used to provide light for tasks (and therefore are used for task lighting). Ideally used for work such as computer work, studying, typing etc. Desk lamps and study lamps are synonymous as these can either be placed on a desk, or can be fitted or connected to a shelf or other piece of the furniture nearby. Usually these are fixed using a clasp or clamp.
Clamp-on task lights occupy very little of the precious desk space but tend to only really fit properly/adjust properly in a limited number of places. Many desk lamps come with an adjustable or bendable neck which allows the light source to be twisted around and aimed at an angle that most suits the person who is working.