What exactly lies between an HDL and a circuit?
are HDLs really used to design digital devices from scratch?


Having done exactly that for many years, I can assure you that, yes,
real chips are developed with HDL.

For that we use, just like with FPGAs a synthesis tool, followed by a team of fellow engineers driving lay-out tools. The difference is that the synthesis tool works with libraries++ from a silicon house. TSMC and UMC are prime examples, but there are other companies providing chip fabrication and each have their own library. By choosing the library you decide if it is going to be a 100, 60, 40 or other nano-meter process. You also have to decide on number of metal layers,


  Are the logical gates ... translated to circuit diagram.


The synthesis tool can produce a logic diagram, but we (as we, designers) rarely look at it. Some other tools read the net-list and produce a schematic which we sometime use for X-propagation tracing, but again that is exceptional.
But the logic diagram itself is not an intermediate step in the design flow. 

++A library is a collection of 'gates' where each gate consist of several transistors which make up a logic function. e.g. a NOT gate but also AND, OR, AND_OR_INVERT, registers with and without reset, with and without scan logic. etc. etc. Also many components exists with different driver strength: BUF, BUF2, BUF4, ..BUF32. 

Along side the logic library you often have other libraries like I/O pad libraries and then there are the analog blocks: Oscillator, PLL, LDO, HDMI, USB...