CLOCK_REALTIME and CLOCK_MONOTONIC with a single call

There's no standard, portable way to do this - clock_gettime is based on operating system functionality that doesn't support this sort of "multi-query". Extending this functionality is non-trivial - and might require developing a driver that will expose this functionality for you.

Specifically on Linux, this might be relatively easy and does not require writing a driver.

On Linux, clock_gettime doesn't actually call into the kernel - it makes use of vdso which allows the kernel to expose information to user-space without having to switch to kernel mode. The classic example of this usage is functions like gettimeofday and clock_gettime - these aren't privileged functions (with the exception of CLOCK_REALTIME, which does require some privileges) and the information can be made available to userspace for efficiency purposes.

You can leverage vdso to access the data directly yourself - have a look at functions in /lib/vdso/gettimeofday.c - which access the tables exposed to vdso to fetch the current time. I linked specifically to do_hres which seems to be the function that accesses the timestamps directly.

By accessing the vdso tables yourself you are minimizing overhead and reducing the difference between your two calls.