Okay you guys... I know how to do this joining technique and darn it, you are confusing me with those descriptions. I'm sure if you are confusing me, then I feel sorry for those that don't know. So let's see if I can chip through some of this confusion.
There is a router bit named a "mortising" bit. This is for creating a shallow mortise (a hole or recess cut into a part) for mortising in hinges and such, not for creating a deep mortise for a mortise and tenon joint. This bit is too shallow to create that deep of a hole. Another problem with trying to use that bit for a deep hole is that is doesn't clear the hole of chips fast enough or well..
Yes, you could use a straight bit, but IMHO, the best router bit for this kind of mortise hole is a spiral up bit, which does clear chips out of that hole efficiently and fast. Yes you end up with a rounded hole, not square corners... But if you clean to hole out with a wood chisel, you can square out the corners of the recess.
If you don't want to take the time to square out the corners, you can use a loose tenon made on your router table... Or you can create a rounded tenon with a tenon jig and a bushing. The length of your tenon is limited to the spiral bit you are using. What this does is mounts to the end of the stock, with the end facing up. You cut down onto the stock with a handheld router, with the tip cutting/creating the shoulder and the edge of the bit cutting/creating the shape of the tenon.
Next is the classic mortising bit, used on a mortiser, like those found as an attachment to jointer/planers. The motirtiser bit its like a long spiral cutter bit and creates a slot with rounded corners. The table of the mortiser holds the stock, moves it onto the bit and slides the stock back and forth to create a slot. Again, you can square out the hole with chisels or create a loose tenon joint with a rounded tenon.
Then there is a mortiser that looks like a small drill press. This uses a mortising chisel bit, that was pictured a few posts back. This "bit" can also be used with a drill press, if you have a mortising bit attachment for your drill press. This mortising chisel bit will not work without one of these two things. An explanation will clear that up. The bit is two part. The inside spins and clears the chips as the chisel drops down and trims a squared hole. The outside collar that is part of the square chisel is held in place and therefore should not spin. The collar of the mortiser or the drill press mortising attachment is what holds the collar of the chisel from spinning and presses it down the hole as it gets drilled. Rectangular holes are made by drilling holes next to each other.
Some people think that since they have a drill press, they go out and buy a mortising attachment instead of buying a mortiser... By the time you get all the parts, you end up paying "about" as much as an inexpensive mortiser. Unless, you buy the bargain brand drill press mortiser attachment ($49). I read a good reputable review of a test from a mainstream woodworking editor who tested 3 drill press mortising attachments, then went back and tested those two named brand and the one bargain brand drill press mortiser attachments against each other... The results where so close between the three, that he picked the bargain brand as the winner. What he did say as a tip for mortisers or drill press mortiser attachments is to go back and buy a quality mortising chisel bit for the size(s) you use most often.
Drill press- drill holes next to each other and clean out with a chisel. Can do same with an auger and brace.
Does that clear things up now? I hope so.