There is difference between them and the difference are 

Rei’sen: she is the pet of yorihime and toyohime known as the watasuki sisters, she lives in lunar capital and she works on the lunar defense corps plus she had blue short hair but she may have same clothes, name and moon rabbit as reisen undongein inaba

Reisen undongein inaba: is the pet of kaguya and eirin student, she lives in eientei and she is a moon rabbit too she had light purple long hair