My advice would be to (1) convert your times (as you get them) to epoch time
and (2) then take the difference of those two. You can then (3) convert the difference into a more human-friendly time format whenever you need.
Example (using your first request):
06:12:23 or epoch time: 1230617543
06:19:41 or epoch time: 1230617981
438 seconds difference or 7 minutes and 18 seconds
You will need to write a program to take in the two timestamps and do the computations, if you plan to do this regularly. Here are a few links to sites that can show you what's involved.
The first website has short, but helpful discussions about how to compute epoch time from "human" formats and vice versa in various languages.
: I'm assuming that you want help doing this with a program and not that you just want us to do the math for you.