Is someone transsexual or transgender if they want to have both genitals?

Wanting to have both genitals is wanting to be intersexed, not a transsexual or transgender. However, people are born intersexed and cannot choose it. So if someone wants to be like an intersexed person, that would be a type of transgenderism.

Intersexed - an individual which which is born with reproductive organs of both sexes.

Transsexual - A person who strongly identifies with the opposite gender and who chooses to live as a member of the opposite gender or to become one by surgery.

Transgender - is a general term applied to a variety of individuals, behaviors, and groups involving tendencies to vary from culturally conventional gender roles.