Could be a little of both. Leg presses can put somewhat unusual stresses on the knee joint depending on the foot position. There's also the potential to load the joint with tremendous forces. If you're stressing that patellar tendon to the point of pain, there is a chance of tendon injury or rupture. These are really bad injuries to try and rehab and would likely require surgery. The good news is that you appear to be OK at this point, but you may have to tread carefully so this doesn't turn into a problem. Tight wraps will be uncomfortable and could leave you a little bruised or sore. Regardless of what is causing the pain, here's what I would suggest:
1) Ice the area daily until any pain or swelling goes away.
2) Keep the weights moderate for more reps on the leg press (nothing that would require knee wraps).
3) Save the knee wraps for heavy squats.
4) If you want something to just keep the knees warm, get some neoprene knee sleeves.
5) Pay attention to your body and if it still hurts, keep things light until it gets better.