Translation:I am studying.
Finally... the present progressive form. I've been waiting this whole time to let the world know that I'm DOING things in Japanese. Presently! And making progress in completing them! Now, I finally can!
...Ah, who am I kidding? I'm not in the mood for doing things. Too much work.
The polite imperative form (Study!) is benkyou shite kudasai. I'm not a native speaker, but I believe that in order to be the imperative form, more is needed than just the -te form (shite). Meanwhile, the continous form (I am studying) is benkyou shite imasu. The -te form is used for a lot of things, but what distinguishes them is what comes after it.
The difference between present progressive and imperative are the usage of the verb to be/exist (iru and aru) after the -te form.
"Study!" - 「勉強して！」(This one I wrote in an informal manner, since it's a rather rough order.)
"I am studying" - 「（私は）勉強しています。」
In the former, the iru (to be/to exist) verb, used for animate objects (and with the formal -masu conjugation), is present after the -te form. That's what turns it into present progressive.
If you’re talking about the difference between “べんきょうしています” and “べんきょうします”, there’s a small difference. The first is the continuous form “I am studying”, as in at this very particular moment I am in the process of studying. The second is the present tense, “I study”. More specifically, べんきょうします is a suru verb- a verb made by attaching a noun (in this case, べんきょう, a study) to the verb する, to do. The present form (formal) of するis します, so the present formal form of べんきょうする is べんきょうします. You then have して, which is the -te form of suru. The present continuous form of a verb in Japanese is formed using the -te form of a verb followed by います. Thus, the continuous form of する is しています, and the continuous form of べんきょうする is べんきょうしています. It’s a little bit confusing, but you’ll get it eventually. Hope I was helpful!
"I'll" is a contraction of "I will" which is a different tense. The "-teiru/-teimasu" form is explicitly as a "current state of doing."
Imagine someone asks you: "What are you currently doing?" You don't say in English: "I'll study." You would say: "I'm currently studying" or "I am studying."
Hope this helps! 頑張ってください。
The てい is what makes all the difference.べんきょうします would be "I'll study" (or "I study" at an unspecified time that could be now, but doesn't have to be so). べんきょうしています however clearly states that this is going on right now. "I am studying" (right now!)