In what ways, if any, does administration of rapamycin *not* mimic calorie restriction?
Rapamycin specifically inhibits the mTOR pathway (mTOR = mammalian target of rapamycin), which has numerous downstream functions including protein biogenesis, regulation of cell cycle, immune function and apoptosis. The upstream effectors of mTOR include growth factors and amino acid availability, so you can certainly see that the lifespan enhancing effects of caloric restriction will be (at least in part) mediated by the mTOR pathway. 

But there are key differences. mTOR also receives signals relating to DNA damage and inflammatory changes (to name just 2) that are essential for healthy survival. So any direct inhibition of this pathway will affect all the functions - I can't find the reference now, but I have definitel read in one of the numerous rodent studies that rapamycin treated mice have reduced immune function (i.e. the lifespan increased effects can only be seen in a controlled lab environment - in the wild mTOR-inhibition to this degree would be a disadvantage).

I think therefore it is fair to say that the effects of caloric restriction on longevity are mediated by mTOR, but administration of rapamycin is not an equivalent treatment.



Update

Really great review came out last month (http://www.ncbi.nlm.nih.gov/pubmed/22500797) - I recommend you give that a skim if you want detail!