WHAT IS MEANT BY "REVERSIBLE ERROR" AND "APPEALABLE ERROR" IN CIVIL CASES SUBJECT APPEAL?

Not all errors provide a basis for an appeal. Appealable error - error that is grounds for reversal - must be significant legal error by the trial court. While you are guaranteed a fair trial, you are not guaranteed a perfect one: "harmless error" is error that isn't significant enough in impact to justify an appeal.

They mean the same thing. Basically, a court error that can be reversed, as opposed to a decision that is moot. Essentially the idea is that if an appellant prevails in appealing the court's decision, can the appellate court's decision reset things to where they were?

Neither of those is a term with precise definition or boundaries. In the context of any specific case I might review the record and advise a client that the proceedings appear to contain "appealable error", meaning that in my opinion an arguable appeal could be taken with a straight face and with some possibility of success. "Reversible error", one might say, is looking at the same question from the court's point of view and asking whether any error in the proceedings so seriously affected the outcome of the trial as to warrant the remedy of reversal. These are not really technical terms, and you will find them used rather casually and with general, rather than precise, meaning.

These are areas where the issue is preserved for appellate review either by motion, objections, or a motion before trial. You can get a remand for a new trial or in a civil case a new hearing on damages based on the type of error.