A stellar cluster or star cluster (sometimes abbreviated SC) 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 young stellar cluster (YSC) is one showing signs of being young, i.e., ultraviolet indicating early stars. In surveys for finding stellar clusters, possible YSCs have been termed YSCCs for young stellar cluster candidates. An embedded cluster (EC) is a cluster in a gas cloud, i.e., one still residing in the cloud of its formation.
A moving group (or kinematic group or stellar association) 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.