These watery baby girl names are almost the same, but Undine is a mythology word-name referring to the spirit of the waters, meaning "little wave" in Latin, first called so by Paracelsus in the 16th century, and Ondine is the same etymology but used in French.
The defining characteristic of an undine is that she lacks a soul, but can gain one through marriage of love. These water spirits have been written about through the ages, sometimes called mermaids and other times water nymphs.
Ondine appears in poem, plays, novels, songs, films, ballet and piano pieces. Undine appears in art, poems, novels, operas, piano and a silent film, as well as being an asteroid. It is also a popular name in comics and video games.
Undine first popped into the SSA in 1912, and hasn't been seen since 1935. Undina is even more rare, never appearing in the data. Ondine jumped in later, in 1961, and is still used. In 2016 it was given to 13 girls, and Ondina was seen only once, in 1968, when it was suddenly given to 15 girls.