In my personal experience, I have never experienced a burning in any other muscles similar to the intense burning that can be felt in the Quadriceps. Again in my experience, the only muscles that come close to the quad burning is the calves and the biceps. For this reason, it is normal to take a break of 3-5 days between leg workouts.
I have never felt burning in my back, shoulder, or arm muscles after pullups. Also, if I max out pullups one day, I can easily return the next day to do more pullups. If I max out my quadriceps one day, I definitely need the next day to recover. There is a difference in how these muscles behave and the recovery time they need. However, maybe this is just me since I exercise recreationally and am definitely not a regular at any gym.
If I max on pushups one day, I can return the next day to do more pushups. Although I am weaker and not able to do as many. In this regard, pushups are similar to pullups.
Even the
Armstrong pullup routine advocates repeated daily exercises with five straight days of pullups to be followed by two days off. Of course, time off is needed for the back muscles to repair themselves but there is a difference from the leg muscles in recovery time. I attribute this difference to "the body is heavy and the reps are few" that I mentioned earlier.
With weight training, it is possible to precisely lift a specific weight to exhaust the muscles. The weights can then easily be changed to further exhaust the muscles for subsequent sets. For exercises based on body weight such as pushups and pullups, it is more difficult to exhaust the muscles with such precision. I have found this leads to a shortened recovery time. Maybe this experience is different for other people, I am not sure.