These are caused by different viruses.
Chickenpox is caused by a virus called Varicella zoster virus (mostly people shorten it to VZV) and this is one of the herpesviridae which is a really massive family of viruses that includes viruses infecting almost every mammal species and lots of reptiles, birds and even fish. The VZV is actually a really complicated virus, everyone knows that when you get chicken pox you get itchy blisters that turn into little pox marks. However what isn’t that well know is that the virus can actually go into a sort of hiding after the chicken pox has passed and the virus remains in a kind of hibernation within the body. In about 10% of people the virus becomes active again later in life (often more than 20 years later) and in this case it causes a disease called shingles and this is quite a painful rash that can form and a person can be stuck with this for several weeks.
Despite this it is better to get chickenpox as a child since getting it as an adult can cause extra complications such as secondary infections or in the case of the virus infecting certain cells of the nervous system it can even cause swelling of the brain.
Measles is caused by a virus called (weirdly) Measles virus this is in a family of viruses called paramyxoviruses the Measles virus is perhaps not quite so complicated in terms of life cycle. The disease in general infects cells starting with a person’s respiratory system (lungs) and spreading to the immune systems cells and the skin cells. Measles is incredibly infectious and it is only because we have such an effective vaccine that cases of measles have been dropping off in recent years. When someone has measles the spots (rash) appear first in the mouth when the spots appear on the rest of a person’s body these spots are sometimes itchy but not always (unlike the chickenpox spots). Symptoms of measles also include fever, muscle aches, runny nose, sore throat and cough. Just as chickenpox can cause complications in a small number of cases so can the Measles virus so can measles. Some serious complications can include bronchitis, pneumonia and a swelling of the brain known as paraencephalitis these complications can lead to death especially in cases where people may not have access to adequate healthcare. In the developed world where we have access to vaccines we often forget how bad diseases like measles can be but measles still causes more than 100,000 deaths a year around the world. For this reason it is important that we support efforts to make vaccinations available for people is less developed parts of the world.