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?
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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.