Rashi (Bamidbar 28:26) says that the reason why Shavuos is called Yom Habikurim is because of the meal offering - the Shtei Halechem - which was the first to come from the new wheat of that year, which is called “Bikurei Ketzir Chitim” (Shemos 34:22), and is referred to in the Haftarah and Musaf as “Minchah Chadashah”
The Bikurim on the other hand, are not necessarily (and according to some should not be - see Minchas Chinuch Parshas Bo, Mitzvah 18:3) brought on Shavuos, and can be brought until Chanukah (Rambam Hilchos Bikurim 2:6), and the reason why they cannot be brought before Shavuos, is in order that the Shtei Halechem should be the first offering (aside from the Omer offering) to be brought from the new produce of that year (Menachos 84b)