Is a transgender woman a hermaphrodite?

No. A hermaphrodite, or more politely, an intersex person, is someone born with both male and female organs. Some intersexed persons can later in life decide which gender they feel like and have the reproductive organs for the other gender removed.

A transgender person is born with either a male or female organs, like an ordinary man or woman. They are gender variant and choose to adopt a role other than that associated with their physical sex of birth. However, most don't get any genital surgery. There is a lack of discomfort with the body itself for the most part.

Then there are transsexual persons who feel they are in the wrong body. This is painful for them. So they live according to their true gender identity and have surgery to make their body and genitals match who they believe they are.