In Ma'oz Tzur, it says:
וּמִנּוֹתַר קַנְקַנִּים נַעֲשָׂה נֵס לַשּׁוֹשַׁנִּים בְּנֵי בִינָה יְמֵי שְׁמוֹנָה קָבְעוּ שִׁיר וּרְנָנִים
What is the Difference between Shirim and Rinanim?
Well, there is the fact that רננים was needed to make the line rhyme. :)
So in Maoz Tzur, the meaning may be something similar: the Sages established Chanukah as a time for singing (שיר) Hashem's praises, and also for getting together in large crowds and talking (רננה) about the miracle.