The finish is usually in reference to the pattern that is embossed onto the card during the finishing process. If you get a hold of a standard bicycle deck and a standard Tally-Ho deck and examine them closely you can see the difference. An embossing pattern is usually done by having a metal cylinder with a pattern on it rolled forcefully against the object that the pattern is being put onto and that object is also against a rubber roller. It's not a chemical but the distinctive pattern being put into the cards that usually causes them to handle differently. The way the patterns interact as the cards slide over each other is what causes the difference in handling. Typically an air cushion finish will allow the cards to trap more air between the cards and make them feel a tad more slippery. You see this effect when you set a brand new deck of bicycle cards down after dribbling them and the top one or two cards slides a bit. A linoid (or linen) finish doesn't do this, and the cards will still slide easily over one another but as a result of the patterns not binding rather than air being trapped. It is often described as having a "smoother" action.
Keep in mind that as new manufacturing processes change this answer will not always be the same, but this was traditionally the difference between the two.