"One twin to another" could be used by a person who is a twin to another person who is also a twin, but not related to the speaker:
As one twin to another, I understand how you feel. I too have a
telepathic bond with my sister.
There is also nothing wrong with using the phrase when speaking of twins of the same pair. Here are some usage examples from Google Books:
This will diminish the competition between the children. Do not
display preferential treatment to either child. Though it is natural
to switch your preference from one twin to another from time to time,
it is important to monitor your approaches.
The issue presented to the Connecticut Superior Court was whether an
equity court has the power to permit the natural parents of minor
twins to consent for the twins to an anatomical transplant from one
twin to another.
.. the pathogenesis is more complex than a net transfer of red blood
cells from one twin to another. Indeed, in most monochorionic twin
pregnancies with the syndrome, hemoglobin concentrations between the
donor and recipient twin ...
Note that all these examples refer to non-specific pairs of twins. The expression "one twin to the other" would more likely be used when discussing a specific, known pair of twins.