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.

Also, desk lamps tend to be more functional looking and are just one color, made from plastic/metal and quite plain. But they tend to be quite cleverly engineered to allow them to be bent into many different positions and angles easily and usually with one hand and a light touch and they also need to have quite a heavy base and be sturdy so that they do not tip over easily.

Table lamps and lighting are available in a huge range of styles, designs and sizes. It is not uncommon for the purely decorative table lamps to have intricately adorned lamp bases carved out of expensive materials such as marble. By virtue of being decorative, table lamps lend themselves to much personal design taste because they serve as ornamental objects as well.

Table lamps also provide a nice source of light with which to highlight objects that are placed near the lampshade and effectively bask in the light of the lamp.

One thing to look out for when purchasing a table lamp is that there should be no glare emanating from the lamp and this is best checked when you are seated, given that most table lamps are placed on a table beside an armchair. Pay particular attention to the lamp height and also to the accompanying lampshade - as a fairly deep shade is needed to avoid glare.

It is possible to coordinate the lampshade of your table lamps with the fabric and furnishings of your room and there are companies that make shades professionally if you want the lamp shade fabric to closely match the rest of the decor in the room.

Task or desk lighting on the other hand will tend to be more functional looking and plain. Nothing fancy or decorative about that.

Commonly, most types of modern task lights tend to be tungsten-halogen lights that come with a dimmer.