If we are using the same terminoligy, then the flow coefficient is usually used to specify the capcity of a valve in the following equation,

Q = Cv*sqrt(dP*62.4/rho)

where,

Q = volumetric flow, gpm
Cv = flow coefficient, gpm/sqrt(psi)
dP = pressure drop through valve
62.4 = reference water density
rho = actual water density
sqrt = mathematical symbol for square root

The coefficient of discharge, or discharge coefficient, is typically used as a linear multiplier of flow area to represent minor losses and friction losses:

Q = Cd*A*sqrt(2*dP/rho)

where,

Q = volumetric flow
Cd = discharge coeffient
A = actual flow area
dP = pressure drop
rho = fluid density

Often times the discarge coefficient is applied when a tank or pipe system is blowing down to represent the non-ideal behavior of the blowdown.  However, the discharge coefficient can also be related to friction and minor losses by,

Cd =  = 1/sqrt(1+fL/D+K)

where,

f = friction factor
L = pipe length
D = pipe diameter
K = sum of minor losses

A good reference for fluid flow formulas like these is Crane's TP-410, available at www.cranevalve.com.  There's also a software version; I have not used that so I can't vouch for it.

JN