Both nebulizers and inhalers give you medicine, but through different delivery methods. An inhaler sprays a quick burst of medicine. A nebulizer creates a mist that is breathed in through a face mask or mouth piece. Both devices have their own advantages and disadvantages.
The main advantage of inhalers is how smallthey are. Granted there are many lightweight portable nebulizers, but these can't slip into your pocket as easily. Inhalers are often recommended for those who play sports, so they'll always have something on hand. Plus, inhalers deliver medicine very quickly. In order to use an inhaler correctly, you must be able to coordinate depressing the canister while breathing inward. Spacers work as an intermediate collection container to hold the medication until you breathe it in.
Nebulizers can take between five and ten minutes to deliver medicine. However, the slower process insures the user is able to take in all the medication, whereas with the inhaler it's easy to lose some of it. Also, inhalers can be difficult for children as they require more coordination. That’s why nebulizers are typically recommended for young children - though they are often preferred by adults as well.
The other advantage of nebulizers is that the mist itself helps to open one's airways so they can breathe easier. Being able to inhale deeply is difficult during asthma attacks and with some respiratory conditions. Nebulizers get the medication directly into the lungs even if you cannot or are too young to take a deep breath.
So back to the original question - do you need both an inhaler and a nebulizer? Though you can get by with either one, yes, it is a good idea to have both. Consult with your doctor to discuss your specific needs to choose a product that is right for you.