No Aspirin and Panadol are two different products. Aspirin is actually the drug's name, whereas the drug in Panadol is paracetamol (or acetaminophen). Aspirin is a good anti inflammatory drug, pain reliever and can reduce fevers. Paracetamol on the other hand is good for pain relief and fever reduction, but not necessarily the best for reducing inflammation.
In addition to this difference, aspirin can be used at low doses to prevent blood clots (like those that cause heart attacks and strokes). Paracetamol does not have this effect at any dose.
Provided you have no allergies, medical conditions (including pregnancy) and are not taking any other medication, it is possible to take both of these medications at the same time, so long as you do not surpass the recommended doses. Please note however that aspirin should not be used in children and teenagers as it is associated with an increased risk of Reyes syndrome (a rare but serious condition that causes swelling in the liver and brain). Instead you can use other anti-inflammatory drugs like ibuprofen (brand name Nurofen or Advil in Australia).
If you do have medical conditions or are taking other medications, see your doctor or pharmacist to discuss your options - they may also be able to help you determine what are causing your headaches which is just as important as treating them.