Internally, this edge selection is converted to node set as well, but including midside nodes which you apparently skipped in your second approach with manual node selection.
Increase the position tolerance and it should work.
You can assign different thicknesses to faces of a compound surface part, but compounding may fail in some cases with surface geometries: Deformation in 2 or more bodies - #10 by Matej and Contact Generations issue Shell_Solid - #16 by Matej
This usually isn’t necessary and you can use tie constraints (unless you e.g. calculate fatigue of welds with some special methods). But you could try enforcing equivalent number of nodes with local refinement and then there is a tool to merge nodes that are close to each other (lie within a specified distance): Model —> Node —> Merge Coincident Nodes.