Dell Optiplex 7010 Intel Core i5-3470 with Celeron Graphics

So I had this Dell OptiPlex 7010 SFF that came with an Intel Celeron G470 and another Dell OptiPlex 3010 with an Intel Core i5-3470 so I decided to swap them. When I booted the 7010, it reinstalled the same graphics drivers that are made for the lower grade processers (Celeron, Pentium Dual) or (Intel HD Graphics for Ivy Bridge) when for the i5-3470 it should download the Intel HD Graphics 2500. (NOTE: The other machine detected Intel HD Graphics 4000 which is for higher grade processors). So is the driver determined by what processor is used or something else internal?