I believe a half round is a half circle. (Cut one layer across the middle and stack it to make a semi-circle) A contour cake is baked in a special pan that has rounded edges instead of sharp edges. It has a soft rounded curve at the edges of the top layer.
The contour pan is a round pan just like any other except instead of a sharp edge, the top edge is rounded off. They are used mostly for fondant because on a regular round pan fondant has a tendency to crack at such a sharp edge. Hope that helps,
Heather
Do a contour pan search on the Internet. Here is one site that carries them, though the picture isn't that great.
http://cooksdream.com/thestore/BD.html
Hugs Squirrelly
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