What is the difference between Shavuos and Simchas Torah if they are both fundamentally celebrations of the Torah?
Another angle, given in various places in Chassidus, and developed further in one of the Lubavitcher Rebbe's talks (Likkutei Sichos, vol. 14, pp. 156ff - English adaptation on chabad.org) is that Simchas Torah specifically commemorates the giving of the second Tablets on Yom Kippur, and so we celebrate it at the end of that season of holidays.
In this talk, too, the Rebbe points out two other related differences:
Shavuos commemorates how G-d gave us the Torah (as an "arousal from above"), while Simchas Torah focuses more on our own efforts in Torah study (an "arousal from below"). (This of course also relates to the idea that Yahu mentioned in his answer, and in particular, to item 3.)
At the original Giving of the Torah on Shavuos, we were tzaddikim. By contrast, on Simchas Torah we celebrate how we became baalei teshuvah.
The difference essentially is:
Simchas Torah is a siyum-celebration of the tzibbur's reading of Torah Shebiksav.
Shavuos is a celebration of Hashem giving us the Torah and of the Maamad of Har Sinai, the miracles we experienced as a Tzibbur at Mt. Sinai.
The are also connections between the two, so you are probably on to something:
They are both celebrated on a hag called "Atzeres".
They both occur after cycles of seven. (Simchas Torah in Eretz Yisrael is actually on Shemini Atzeres and Shavuos is after the complete counting of the omer cycle of 7 times 7).
Shavuos occurs at the beginning of the human food harvest (wheat) and Simchas Torah occurs at the end of the entire harvest process.
An answer from here although it is a Parable more than an answer. http://www.aish.com/h/su/saast/48967086.html