The other member of the Rebate - Rabbet - Fillister family is the Shoulder Plane. These are finishing planes at their finest. Very low angle blades extending through the stock such that the cut can shave right up to the corner of the cut.
The shoulder plane is used after the rabbet and/or fillister has done it's job. It's also used when making tenons with a backsaw. It's a precise plane, allowing for very thin shavings to be taken, leaving a right angle, clean of marks and ready to be glued or admired.
Because the mouth of the shoulder plane is open on both sides and the body is fairly narrow and not very high, these are typically made entirely of metal or cased in metal. They're pricey but well worth the investment.
I have a Stanley 90 and a 93, both old ones and well worn in. The blades only get a touch up as needed so I expect them to last for decades to come. They may not be lookers, but who cares? They do the job just as well as spiffy clean nickled versions do. Their main purpose for me is cleaning up old joints on old furniture I'm fixing up. They are essential.
Many people complain of the rough surface left by their rabbet planes or fillister planes. That's where the shoulder plane comes into play. If you need to clean up the joint, to correct a mistake or to repair an old surface, a good shoulder plane will do the trick for you. But... most glue joints don't require a perfectly smooth surface so why worry about it unless you really have to. It's not the mating surfaces of the average mortise and tenon that need attention, it's where the two meet that should be a clean 90 degrees. A properly set rabbet plane can often do the job in soft woods or the softer hard woods such as cherry or butternut.
One word on sharpening shoulder plane blades. There are three edges to consider. The lead cutting edge and the two side edges. Opinions differ here. I sharpen all three. The lead edge gets the full treatment. The two side edges act like scrapers so I don't go for the super sharp edge, just a sharp enough edge. I don't use magnifiers, microscopes, waterstones or obsess over sharpening. If it cuts, it works.
We could go on into carriage makers rabbet planes, ship rabbets, jack rabbets and more but you gotta stop somewhere.
Till next, Gary.