The term greased line means different things to different people. However according to the man who developed the idea, or at least the man who interpreted the man who developed it, it is simply presenting a fly to a fish broadside without drag. Because this was developed at a time when lines tended to gradually sink throughout a day of fishing this angler A.H.E. Wood would dress his lines to make them float all day. thus the term "greased" line.
These days the term is mostly used ( incorrectly) to define any floating line method broadside or not, with drag or not. Others call any surface fly presentation " greased line".
I think that because Wood fished the same area of the river all the time that he knew exactly where the fish held and therefore fish specific lies not just entire runs and that He actually fished the flu more down than across with the fly broadside to the fish without any drag. However this is not a dead drifted presentation as this is a very controlled presentation. He fished with tension on the line but without drag on the fly..
"Never be afraid to show love" Frank Moore