for mortise & tenon typically the tenon is not as thick, and not as wide, as the workpiece. i.e. is is cut on all four sides, to fit the mortise pocket.
the dado is one long groove cut to width for the joined pc.
a dado does not have to continuous from one end to the other - to make those I use a router, and clean up the ends with a chisel.
in cases, you can round the ends of the joined piece - that depends on how "hidden" the corrners are...
here's a simple table I made for our daughter - it's a 'custom' size to fit a specific area; standard tables didn't fit....
the upright legs - a dado in the front / rear, the side legs fit into the dado.
the "skirt" between the uprights is a blind half-lap joint. it was a bit thin on the back side, so I glued in a small "doubler" for reinforcement.
the whole thing is glued - not a single nail or screw anywhere.