The moving-cluster method is a method of determining the distance to grouped 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 together, so this applies to them, if they are not too far.
The method consists of determining a convergent point, a point in the celestial sphere to or from which the stars appear to be moving, which is presumed to a direction in the sphere (in the same sense that the apparent meeting point of the rails of a straight railroad track is the direction to which the track leads). Given this determination of their direction of motion, the ratio of the transverse velocity and radial velocity can be worked out, and with radial velocity measurements by Doppler shift, the transverse velocity can be deduced, and by comparing that to the 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.
The moving cluster method depends upon mathematics and probability to make best use of the observations in light of random measurement errors, and averaging methods have been developed aiming to get the best use of observations. The method became less commonly used as other distance-determination methods improved, and observation improved, e.g., the accurate astrometry of Hipparcos. However, more recently the moving cluster method has been retried because the improvement in astrometry also improves this method's results.