No difference, because they're both wrong! You want to say, "to study it" or "to study about it." You can only say "in" if you're talking about, for example, a library ("She studied for two hours in the library"). You can "study at" a particular school, university, etc. ("He studied history at Harvard"). And you can "study with" a friend!

I wouldn't mind hearing them said though a bit odd, they are. "Study on it" sounds like "I study on (meaning "about") this subject", after all, study could be intransitive. This is why I would say Jura doesn't really study on grammar and as a result she doesn't know what "grammatically" means.

Muchas gracias!

Both are grammatically incorrect.