Hi Steve - so in your last model there you've got an open surface instead of a solid.

What you probably want to do is to make it into a solid first before you actually cut the rectangular hole in it - one way of doing that easily with that shape is to select it and run the Construct > Planar tool, which will build trimmed planes through any planar openings and join them in to seal them off, then you'll have a solid.

Then when you do a boolean on a solid with a curve, the result will be a solid too - when cutting a volume the curve will basically leave behind the "side walls" parts of where it was extruded. This won't happen if you are not cutting a solid object.

Basically the booleans are kind of more oriented towards working with solids, you can also use the Trim command to cut things up as well in addition to the booleans, but booleans are kind of like a "batch mode" trim, where they not only cut things up but also decide which pieces to keep based on which volume the pieces are in, if that makes any sense.

So basically when doing booleans it tends to be easiest to be doing the boolean on a solid object as the base object instead of an open surface that does not define a totally closed volume.

Hope this helps!

- Michael