Actually yes - the H stands for hardware: that's any kind of digital logic. You just need a different "back end" and then in theory the same model can run on various targets - in fact there is a whole business model around getting a design up and running on an FPGA and then porting it to an ASIC once you can justify the volume.
You can most certainly build ASICs in VHDL. VHDL is not restricted to any target technology. There are (commercial) tools which allow you to synthesise the masks needed for ASIC production from RTL (register transfer level) VHDL code given a cell library for your target technology. See random Google search result [1].
No it is not entirely different. Don't forget that FPGA is originally made for prototyping an ASIC, and HDL came out to configure digital circuit before FPGA is invented.
Of course an ASIC cannot be made with only HDL, and not sure if it is a correct expression to say 'to write' an ASIC.
