The moving-cluster method is a method of determining the distance to a group of stars that are moving at the same velocity and are sufficiently close to us that their proper motion can be determined. Open clusters are so-grouped and generally moving as a group, so this applies to them if they are not too distant.
The method consists of determining a convergent point, a point in the celestial sphere to or from which the stars appear to be moving. If they are moving away from that point, the method works on the assumption that they are moving in a direction parallel to our line of sight toward that point. This is analogous to the fact that the direction at which we see the apparent meeting point of the rails of a straight railroad track is virtually parallel to the direction of the rails. Given this determination of their direction of motion, the ratio of the transverse velocity and radial velocity can be worked out, the radial velocity can be measured by Doppler shift, and the transverse velocity can be deduced. By knowing this actual transverse velocity and the measured proper motion, the distance can be determined.
I've seen the phrase convergent point method described as synonymous, but one source calls them "closely related". I've also seen reference to convergent point method as a means to determine which stars are in a cluster; basically, their velocity appears similar and they do have such a convergent point.
The moving cluster method's accuracy is improved by probability analysis of measurements of numerous stars in the cluster, in light of random measurement errors and of the stars' individual peculiar velocities. The method lost favor as other distance-determination methods improved, such as with the modern precise astrometry of Hipparcos. However, it has more recently sparked interest because the improvement in astrometry also improves this method's results.