Does contracting Rubella give one some kind of immunity to Measles and vice versa?
Short answer: No, there is no cross immunity between these two diseases. Having the same symptoms doesn't mean that diseases are related. 

Both have in common that they are caused by viruses, but similarities end here. Rubella is caused by the rubella virus, which is the only member of the genus Rubivirus and belongs to the family of Togaviridae and are encapsulated positive strand RNA viruses.

Measles on the other hand are caused by the measles virus, which belong to the genus Morbillivirus within the family Paramyxoviridae and are negative stranded enveloped RNA viruses.

Historically speaking, the measles vaccine was available first in 1963, with mumps following in 1967 and rubella in 1969. All three are attenuated live vaccines which have been combined into a single vaccine in 1971. The sequence of this developments also shows that there is no cross immunity. You wouldn't develop another vaccine, when the disease is already covered by another. Drug development is a very expensive business.