The term current start date refers to the deliberate and calculated estimate of the specific point in time at which the activity and or schedule activities is expected to be completed. The term current finish date is somewhat ambiguous and more properly phrased and termed date at which the activity is currently expected to be completed. The date is a time in the future, not at present. An appropriate estimation of the current finish takes into account any and all work and work progress that has been completed at the current point in time. The current finish date is, by definition, a fluid estimation. At various points throughout the life of a project a current finish date may be reassessed as additional work activities have been completed, as delays may arise for one reason or another, or in the fortunate (and far too few and far between) instances in which a project team may actually find itself significantly and unexpectedly ahead of schedule.
This term is defined in the 3rd edition of the PMBOK but not in the 4th.