As I understand it the spot light is a controlled light within a cone, the camera doesn't "see" the light bulb that is the source of light so you don't get the bright circle at the source. This prevents the spot source being seen even if it is pointed at the camera.
The built-in lights seem to have a fixed amount of light to emit, by reducing the size (that is size not emission value) to 0.0 all the light is concentrated to the one small area at the location of the light. By increasing the size of the light the same amount of light is dispersed from a greater area and appears dimmer at any given point.
Mesh lights work the opposite way and are based on mesh size, with the entire surface of the mesh emitting light, the bigger the mesh the bigger the source of light so more light is emitted throughout the scene.
I consider the built-in lights as an easy to use leftover from blender internal. The first version of cycles (2.61) had initial support for sun, point and area lights added just before release, with spot support added in 2.64, so I think they were mostly added as a convenience. The fact that their functionality is mostly opposite to mesh lights leaves no easy way to convert one to another.
I go with use built-in lights for BI and for cycles use mesh lights.
To better represent the point light a sphere mesh can be used. A proper spot light can be made with a sphere emitting from inside an open ended tube.
At size 0.0 all lights are concentrated to a point of light.
At size 5.0 the same amount of light is dispersed from a larger area and is almost invisible. Notice that the area light still emits a fair amount of light when it is large. It's entire surface is the source of light, while the others are just origin points.
Scale the mesh object to 0.1 and get a tiny source of light, but at a scale of 5.0 you have an almost white scene. Applying the scale doesn't effect the amount of light emitted.
Mesh light at scale 0.1
Mesh light at scale 5.0