HELP differentiating b/w Base and Nucleophile

When given an alkyl halide, depending on the reagent (strong nucleophile, weak nucleophile, strong base, or weak base), the reaction can undergo SN1, SN2, E1, or E2 mechanisms, right? I know SN1 and SN2 reactions require nucleophiles, while E1 and E2 reactions requires bases. My question:

If given an alkyl halide and a reagent, how do you determine whether the reagent is a nucleophile or a base?

This is confusing to me because the reagent can be both a nucleophile and a base at the same time. If a reagent has the properties of both a nucleophile and a base, how do you tell whether to use SN1, SN2, E1, or E2?

The University of Colorado has a flow chart regarding this topic:
http://walba.colorado.edu/substitution%20and%20elim'n%20'02.htm

The University of Eastern Illinois also has one:
http://www.ux1.eiu.edu/~cfthb/classes/2440/subst_elim.htm

Still, I am stumped on how to differentiate between a nucleophile reagent or a basic reagent. Can you help me out here? If not, can you point me in the right direction? Thank you for your time.