Leebo
at 2020-07-23 12:47:23 UTC
They're both very common words that don't really have a politeness or formality distinction between them. The bigger differences are in where they commonly appear. For instance, it's not very common to refer to an individual person as 女子. But when referring to groups (without much regard for specific ages), 女子 is quite common. So you say 女子トイレ for "women's restroom" and not 女の子トイレ. You would say 女子バスケットボール to talk about women's basketball.
Here's a monolingual thesaurus entry. It might be above your level, but it does have a chart at the bottom with concrete examples of places where you can and can't use various words for girls and women.
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Difference between 女子・女の子 and 男子・男の子
Im not really sure what the difference is, but maybe the ＿の子 is slightly more polite than ＿子?