Jisho

My bad, I meant to say difference between しょうじょ and おとめ. Sorry 'bout that.

少女 is a word that refers to girls that are somewhat between children and adults. It has a slightly romantic (referring to this definition: of, characterized by, or suggestive of an idealized view of reality) feeling to it. As such, it's not used all that often in everyday language.

乙女 is a word that is used almost exclusively in written language. It has a poetic feeling.

You didn't ask, but hear are some other words for young girls you will hear:
女の子 - used for a wide range of young girls in everyday language
女児 - a word used to refer to elementary school / primary school aged girl (mostly written language)
女子 - covers a wide range of girls from elementary school up, but it has usages that are different from 女の子 (for example, you say 女子トイレ and 女子バスケ部 and not 女の子トイレ or 女の子バスケ部)

Source for most of this: https://dictionary.goo.ne.jp/thsrs/4849/meaning/m0u/%E4%B9%99%E5%A5%B3/

When I said "As such, it's not used all that often in everyday language." for 少女, I just mean relative to neutral (non-romanticized) words such as 女の子 and 女子

But, is there a difference in meaning between the two readings of 「少女」, 「しょうじょ」 and 「おとめ」?

Ah OK, I understand now. Both 「少女」 and 「乙女」 can be read as 「おとめ」, but only 「少女」 can be read as 「しょうじょ」. So when Leebo writes, "乙女 means...", they mean the reading 「おとめ」, which can be used for both words.

おとめ is a non-standard reading for 少女, so if you ever see it, it will almost always be marked with furigana.