A stellar cluster or star cluster is a general term including both globular clusters and open clusters, consisting of groups of stars near each other, with other similarities that suggest their formation is from a single cloud. The distinction between globular versus open clusters is that the former are tightly bound by gravity and the latter is more loosely bound.
A moving group or kinematic group is a looser group of similar stars that are generally moving together. Such a group is presumed to be the remnant of a stellar cluster. Often the stars are old, perhaps older than typical for an open cluster.