Durations

Duration: parallel yield curve shift
D = -(1/P)(dP/dr)

Modified duration:
MD = -(1/P)(dP/dy)

Macaulay duration: under the mindset of "duration<->time to maturity"
MacD = MD*(1+y/2)

Effective duration:
For securities with embedded options

Spot rate duration:
Spot rate is changes (not shift of the entire yield curve). Usually found numerically.

Factor duration:
Price change with respect to some factors other than rate

Also, since D = (-1/P) (dP/dy) and convexity C =  (1/P) (d^2P/dy^2), it can be shown that

dD/dy = D^2 - C