Maneru vs manesuru?

What's the difference between 真似る and　真似する？

I'm just wondering if they are the same word or if there is an actual difference (in meaning or nuance). It seems weird to me that there would be two different verbs with the same kanji stem that mean "to imitate".

They mean the same. "mane suru" I'd say is the shortened version of originally "mane wo suru," "do imitation" = "imitate."

Both are the same if you make it "mane wo suru". But there are slight differences in usage between 真似る and　真似する.

真似る is usually used with I, i.e. "watashi ha kare wo maneru=I imitate him, watshi ha anata no kakkou wo maneta=I copied your style, etc.".

And　真似する is usually used with you, (s)he, they, etc., i.e. Anata ha watashi wo yoku mane surune=You imitate me often, "kare ha watashi wo manesuru koto ga suki da=he likes to imitate me., etc.

I thought 真似る is the abbreviation of 真似する in colloquial style...
So I think 真似る is more informal/casual than 真似する.

Anyway, both are a bit familiar, so 真似をする is better to write in polite Japanese, as AK said.

ものまね (imitation of someone's action) can be used to mention both nice and poor imitation, but 猿まね [ さるまね ] is a contemptuous word to mean copycatting.
Sometimes the noun まね / the phrase まねする has negative or sarcastic meaning or implication, like "mimic" in English, used to mention poor or indiscriminate imitation.
The noun まね is also used to mention unfavorable deed.
We say 「ばかな真似をするな！」 ("Never do (such) a foolish thing!" "Don't be foolish!")
but we do NOT say 「ばかを真似るな！」 .
When a person says 「なんの真似だ？」 he/she is highly likely to be irritated at incredible deed of another.
I suppose the verb まねる can be rather neutral.

Depending on situations, に 倣う [ ならう ; usually in hiragana] or を 手本 [ てほん ] にする / とする is better than を 真似る [ まねる ].
Unlike 習う [ ならう ] as in 「日本語を習う」 , 倣う takes a particle に and can be used about a person.
: 例 [ れい ] にならって問いに答えなさい。 (Answer the questions, following the example.)
: 彼にならって青い旗 [ はた ] を振って [ ふって ] ください。 (Just as he does, please wave a blue flag.)
: 彼女の作品を手本にして、折り鶴 [ おりづる ] を十羽 [ じっぱ ] 折りました。 (I made ten paper-folded cranes, taking her work for a model.)