Julie,
   Most of the immunities passed on to the baby through brmilk are passive
immunities. You ask > if mom has actually had a disease, such as measles or
mumps, will the protection she passes to her child be different than if her
immunity is from the vaccines?<  Yes
The antibodies mom makes for the measles or the mumps pass through the milk
and protect the baby. The baby may get a mild case but may not develop active
immunities. It is the mother's antibodies that attack the disease so the
infant doesn't have enough eposure to make her own antibodies.  This happened
with a friend who thought her bfing daughter had the chicken pox. She even
developed a few pox. However when she went to school she *caught them again.*
 Obviously, she did not make her own immunities.  The idea behind a vaccine
is to generate active immunities in the host. I'm sure breastmilk does this
with some diseases but certainly not all. (for example: how do cholera
antibodies get in the breastmilk if the mom never had it or was never
vaccinated?)
There was a problem several years ago with children who had received the
measles vaccine before their first birthday. Their immune system was not
developed enough to have immunity from the vaccine and when they reached high
school age: there were measles (Rubella) outbreaks everywhere (well here
anyway). All our high schools now require boosters before the kids begin
their freshman year.
Marie Davis
Home today with a housefull of kids with colds (me too-- sniff)