You don't have bases and then you have another class that is nucleophiles, the two groups overlap - there is just a question of strength.
Generally, a strong base is a strong nucleophile IF it is not hindered (one important exception if you're still on E1,E2, etc is hydride, hydride, such as NaH, is basic, not nucleophilic). For example, Tertbutoxide is very basic, but it is so bulky it is not nucleophilic. Methoxide is 'nearly' as basic, but it is nucleophilic because it is not hindered.
There are other systems, such as hard and soft theory of nucleophiles/electrophiles and there are more accurate ways to classify a nucleophile such as by the ease of polarizing the molecule or atom, but for now, that should help.
If you already knew that though, let me know, we can go over more.