If PS and VS have different registers: How are they called? Which register is set if I call
SetVertexShaderConstant and which one is set by calling
SetVertexShaderConstantF will set the vertex shader constant registers (c# in the msdn link).
SetPixelShaderConstantF will set the pixel shader constant register (c# in the pixel shader version of your link)
There are also integer and boolean versions of the above (same as above but with I and B instead of F, and i# / b# on the msdn pages).
The pixel and vertex shaders both have their own float, integer, and boolean constant registers. They are completely separate, the pixel shader cannot access data in a vertex shader constant and vice versa.