Three wire vs four wire feed remote sub panel
Back in the old days, grounds didn't exist at all.  Mains electrical was wired as an isolated system.  It still is, but now we've added ground as a safety shield.  

When they started to require grounding, they went to pains to make sure they weren't mandating old work be retrofitted.  Old work is "grandfathered" - if it was legal at time of installation, it is still legal today.  However grandfathered work does not have the safety features now required; because of that many upgrade it voluntarily. 

In some cases: dryers, ranges and subpanels, they allowed groundless connection, but attached ground to the neutral wire "since they're the same back at the panel".  That proved to have problems, as you mention in comments. Notably a simple wire break of the neutral wire can result in all things which are supposed to be grounded now  being electrified.  

Now, in a subpanel, it is normal for the load not to be balanced, and for there to be say, 20A of flow on the neutral wire.  What happens when that neutral breaks?  Now the current is trying to return via the grounding rods. And at 25 ohms, which is the max resistance allowed for a single ground rod to be acceptable, that doesn't have a chance of safely earthing that much current.