to me, "get tired" refers to a point in time after which you are tired, and "grow tired" refers to a period of time during which you become tired.

Hey, in my opinion I would have to say: no there is not a difference. But, most people use "get tired" in conversation. I rarely every use "grow tired." Example: I got tired of watching tv. (That is pretty normal) Example: I grew tired of waiting. (Not used very often, more so in novels/books.) Hope that helps.