Conductive means the paste will pass electricity. Capacitive means the paste has a high dielectric constant and can act as a capacitor. If you put conductive paste on traces or joints of the boards that have exposed metals that are energized when in use, you short them out and cause issues. If you put capacitive paste over closely-spaced pins or on top of capacitors/electrical components, you can form a capacitor and inadvertently pass high frequency (digital, for example) signals to cause issues.
A paste that is non-conductive and non-capacitive means that it has low conductivity and low dielectric constant so that you can use it and not worry about shorts if it ever touches electrical components or pins, etc.
As for the spread...