I used to work a 36 hour shift with a 2.5 hour commute on either end. I usually did get some sleep during the shift but on the whole it wasn't that bad. I'd get home, have dinner with the family and have a good night's rest and I'd be good to go the next day for my regular 40 hour work week. I did that for the better part of 2, maybe 3 years.
We were busy most of the time but it on the whole, I had a good time. The worst shift I'd ever done was an 84 hour shift. 3 back to back 24's and a 12 hour. In that time I stayed on one truck, had 5 partners, and ran too many calls to count. Fortunately, we did get some sleep every night but we also ran some calls every night too... sleep did happen, but it wasn't quality sleep. That was not the most tired I'd ever been though.
The most tired I'd ever been was when I was working graveyard and had PM clinical. For the better part of 4 weeks I survived on 2 two hour naps on either end of work or clinical and trust me, while I didn't feel tired, I was extremely unsafe... an incident waiting to happen. Fortunately my instructor pulled me off the floor and I was sent home. I got a good night's sleep and that's when it hit me... I really was way too tired to be safe. Now I know my own limits and I work well within them. I have done extremely well since.
The point of this is simple. Just because you don't feel tired after a long shift doesn't mean you're 100% safe to do the job. Pay attention to how you truly feel and sleep deprivation can be very, very insidious. Feeling exhausted is actually a good sign that while you're tired, you're not all that sleep deprived. Not like I was. If you need to take a day to recover after a shift like that, take that time. Otherwise you'll become progressively more and more sleep-injured. At some point, you'll be so injured that something seriously breaks and it'll take a long time to recover and you may not ever recover to 100% of what you used to do.
And yes, I look at being sleep-deprived as being sleep-injured.