Game time works the same for all games, regardless of Real Time or Turn Based. There is a base time, and a time per move.
The base time is the amount of time that each person is given at the beginning of the game. In the case you listed, it is 36 hours.
The time per move is the amount of time that will be added back to the player's clock after they make a move, up to the base time. This is the 12 hours.
So, let's say that you start this game. You have 36 hours to make a move. You take 1 hour to make that move. Your time will be at 35 hours. But, as soon as you make the move, 12 hours is added to your time. But, since it caps at the original time, you will have 36 hours to make your next move.
Then let's say it takes you 24 hours to make your next move. Your clock will have run down to 14 hours. Then, 12 more hours will be added, bringing it up to 26 hours. Let's say another 22 hours pass (you really haven't been playing 2 moves per day
) It will have run down to 4 hours, but back up to 18. Then you make moves faster than once every 12 hours. Your clock will eventually climb back to 36 hours, but never more than that.
The difference between clocks on turn-based and real-time is the amount of time. Turn-based games have time per turn in the range of 8-48 hours per turn, whereas real-time games have these in the minutes range. It's been a while since I've done real-time, but I seem to remember examples being something like 3:00 minutes base time + 1:00 minute per turn. So, at most a player will have 3 minutes to think when it is their turn, but to avoid running out of total time they must average a move every minute.
Running out of time automatically causes penalties. In addition, if you have negative time any player at the table can expel you.
Now, as to the comment about the clock stopping. This is a new feature, "fast-paced turn-based." The time still works the same: there is a base time and a per move time. The difference, though, is at a certain global time, all player's clocks will stop counting down. (I say all players, as there are some games with simultaneous play that have more than one person's clock counting down at the same time.) The time that this happens is set by the table creator, not per player. The time shown will be adjusted for local time zones, but it happens for the entire table at the same global time.
Does this clear it up? Any more questions?