Okay I did a "google" search and found a web site that that explains all the types of drill presses. According to this web site, the simple definition of being hand fed and driven by a belt seems to define a "sensitive drill press", not necessarily its size or speed. I have included the WEB URL below... check it out as it has pictures, etc. The text from this web site giving the definition of a "sensitive drill press" is as follows:
The upright sensitive drill press (Figure 1) is a light-duty type of drilling machine that normally incorporates a belt drive spindle head. This machine is generally used for moderate-to-light duty work. The upright sensitive drill press gets its name due to the fact that the machine can only be hand fed. Hand feeding the tool into the workpiece allows the operator to "feel" the cutting action of the tool. The sensitive drill press is manufactured in a floor style or a bench style.
http://its.foxvalleytech.com/MachShop1/drillpress/drilltypes.htm