There are two possible definitions of base:
Substance which accepts a proton throughout the course of the reaction (catalyticly or stoichiometricly). This is basically the Brønsted definition. To accept a proton, the molecule in question needs a lone pair whose energy level and orientation is in a good range for a proton to attach (e.g: ammonia: good; phosphane: bad). We could also extend the definition Lewis-style.
Substance which generally may accept a proton in reactions. This is still basically the Brønsted definition only without the requirement of it actually happening. The molecule needs a lone pair whose energy level and orientation is in a good range for a proton to attach even if it doesn’t happen. We could also extend it to a Lewis-style definition.
Applying the first definition, nucleophilic substitution reactions usually do not require bases. However, the molecules that attack are generally bases: A nucleophile generally needs an accessable lone pair, as would a base.
Consider the case of an alcoholate. If it is methanolate, it is small and can attack nucleophilicly. However, we also know that it can act as a base to be protonated to generate methanol. Depending on the substrate, it would choose to do substitution or elimination reactions.
If the alcoholate is tert-butanolate, we have a large molecule. Technically, it still could attack as a nucleophile. However, it is usually too big to attack and rather abstracts protons to allow elimination reactions.
You cannot really draw a line. Both are bases, both could be nucleophiles.