Center bearing vs. Clear Span floors -- Span Tables
Clear span is typically taken to be the distance between the supports, not the overall length of the joist. In some codes, you add a small amount to the distance between supports to account for bearing.
I think the tables you are referring to are used to compute the load on a joist or beam. If the floor above is clear span (no intermediate support), you use one value for the psf loading oin the joist. If the floor above has an intermediate support, you use a different value for the psf loading of the floor. This affects the loading of the supporting beam, so the beam may be sized differently depending on the loading condition.
As for the second question, if you had two joists that spanned 30 feet with an intermediate support (such as my house), the clear span of each joist would be the distance between the center support and the wall, which would be approximately 15 feet. It would not be the length of each joist, since the joists would typically overlap a foot or so beyond the center support.
As for the difference between two 15 foot joists that spanned 30 feet versus a continuous joist that spanned 30 feet, the moment curve for the continuous joist is totally different than the moment curve for two separate joists. The reason is that in the case of two non-continuous joists, loading on one joist does not have any effect on the second joist, since the joists are not connected. Each joist is treated as a single simple span beam. In the case of a continuous joist over a supporting beam, load on one side of the joist definitely affects the other side of the joist, and under certain conditions you can get negative moment over the top of the support. So the sizing of a continuous joist may be different than the sizing of two independent joists.