What is the difference between a non-directional signal and an omidirectional signal from a radio aid?
"Omnidirectional" may not be the most descriptive word for the actual radio signal emitted by a VOR, as contrasted with the signal from a NDB.  We could note that a VOR and a NDB actually both share the characteristic of broadcasting in all directions, as opposed to the narrow beam emitted by a landing approach aid, or the characteristic pattern emitted by the "four course" radio ranges of long ago.

But as for the difference between the radio signals emitted by a VOR and a NDB-- 

Think of the signal from a VOR as a collection of beams radiating out from the transmitter.  Each beam carries data: it is encoded with the azimuth from the station.  You can easily find more information about how this done: in actual practice the azimuth information is encoded in a phase shift between two different signals.

With a NDB, we also have beams radiating in all directions from a transmitter, but all the beams are the same.  That's why you can only get a relative bearing from a NDB.