The gemara in Rosh Hashana 29b,asks why don't we blow shofar on Shabbos and answers as follows. The pasuk says יום תרועה and it also says זכרון תרועה. The first is when RH falls out during the week the second is when it falls out on Shabbos. The gemara then asks, if so why in the Beis Hamikdash do we blow on Shabbos? Also, what is the problem with blowing on Shabbos it is not a melacha? The gemara therefore rejects the first answer and answers in the name of Rava that it is a גזירה tha maybe you will carry the shofar.
The Yerushalmi however, sticks with the Bavli's hava amina. It doesn't ask the Bavli's questions and doesn't offer the גזירה reason. According to the Yerushalmi, it comes out min hatorah there is no chiyuv to blow shofar on Shabbos.
There is a big nafka mina between the 2. R' Zvi Pesach Frank has the following question. There was a machlokes in his day whether you should to blow shofar in Yerushalayimn on Shabbos (ואכמ"ל why). R' Shlesinger held that it was allowed and therefore he blew shofar on Shabbos. R' Frank asked whether other people should go and listen and be יוצא the mitzva. The whole question only is relevant according to the Bavli, according to the Yerushalmi there is nothing to talk about as there is no chiyuv on Shabbos.
He points out that according to the Bavli (that it is only a גזירה) it is related to a machlokes Tosafos and the Ran by Succa. When the chachamim say not to do a mitzva and you do it, are you mekyame the mitzva? Tosafos Succa 3a sys no, the Ran there argues and says you are mekayem the din doraysa. The same here by shofar. According to Tosafos since לשיטתך R' Shlesinger is violating the din d'rabbanan he and you are not יוצא even the mitzva d'oraysa.