Nucleophilicity is a kinetic term (how good something is at seeking out an electrophile). Basicity is a thermodynamic term pertaining to an equilibrium. Strong bases aren't always good nucleophiles because they could be very bulky (ie LDA or tert-butoxide) and thus inhibit the rate at which they seek out electrophiles. therefore we can't always say there's an exact correlation between the two terms.
Solvents also affect nucleophilicity, specifically that of the halogens. Protic and
aprotic will thus exhibit different halogen nucleophile trends due to the fact that a protic solvent will more readily solvate a F- ion and thus inhibit it's ability to act as a nucleophile. Therefore, the I- ion will be a better nucleophile in protic solvents and the reverse is true for halogens in aprotic solvents
Does that help?