日本語を勉強します sounds you are studying Japanese not Chinese, 日本語の勉強をします sounds you are studying Japanese now and after that you may be studying Chinese probably. Those are one of those examples for making the slight difference clear. Both are natural and almost the same.

I think they mean the same basically. Some Japanese noun can be a verb with する, for example, べんきょう(noun) + する(do) = べんきょうする(verb). In English, too, there are noun and verb but in this case the word is the same, "study". So, the structure of these sentences are: 日本語を is object, 勉強します is verb. 日本語の勉強を is objegt, しますis verb (like "do the study of Japanese). I hipe this was helpful.