Wouldn't the first be called dado planes, cross grain for shelves typically? Not sure if any of my dado planes are skewed.
76 p., illus., 21.5 cm, trade catalog
archive.org
No
While Dado planes were also used cross grain they had Knickers for both sides of the cut , a shoe to limit depth sometimes, and a stepped sole. The sole/knickers/blade cut a very defined width.
I was specifically talking about Cleve mentioning cleaning up tennons, the plane used to do that is a bench or block Rabbet plane typically has just one knicker on the inside of the cut. Typically left side but there were matching sets many times with the blade skewed the opposite way/knicker on opposite side. The blade was much wider as the right side may hang in the air or the cuts could be quite wide. The sole was not stepped. This type of plane was not conducive to a wooden body due to stress of so much wood cut for the blade to extend to the edge so most examples are going to be cast iron or dovetailed infill planes.
Here is a block version, knicker under the phillips screw
The cleaning of tennons in the wooden plane era was typically done with slicks. And also the work on non visible items such as tennons was much cruder/rougher than most modern woodworkers would think, and backed up with draw bored pegs.
The plane picture posted by the op would only be used with the grain.