There is no principal difference. Usually it is assumed that gravity anomaly is produced from some body (bodies) under study (useful signal) and disturbances represent different kinds of noise. I propose that our paper from the RG DataBase (see below) will be interesting for you:

Al-Zoubi, A., Eppelbaum, L., Abueladas, A., Ezersky, M. and Akkawi, E., 2013. Methods for removing regional trends in microgravity under complex environments: testing on 3D model examples and investigation in the Dead Sea coast. International Journal of Geophysics, Vol. 2013, Article ID 341797, 1-13, http://dx.doi.org/10.1155/2013/341797.

Torge, in "Gravimetry" (de Gruyter, 1989, p. 43), gives a nice summary of these two concepts. Basically, the gravity disturbance is the difference between measured gravity at a point (P) and the normal gravity AT THAT SAME POINT P, while the gravity anomaly is the difference between the observed gravity at P, and the normal gravity on the geoid (Q), the point where the normal to the ellipsoid at P intersects the geoid.

I agree with Bill Kearsley's answer.  Except that that it can be generalised for gravity anomaly as: the difference between real gravity on the real equipotential surface W=const.=Q and normal gravity on the the intersection of normal to reference ellipsoid and the normal equipotential surface U=const.=Q.

True- thanks Peter

Hi ,ALL

Thank you very much for all

Special thanks to Dr.Kearsley and Dr.Peter

And  i wish to have connect between us continuous