Yes the 27” iMac PSU, 310W is the same for 2009/10/11 systems. Just like the 21.5” iMac PSU, 205W is the same across the 2009/10/11 systems.
The older 2009 20" PSU, 180W and 24" PSU, 250W are different!
And the 2007/08 systems are yet different again! 2008 20" PSU, 180W & 2007 20" PSU, 180W are each different from each other (wiring difference) yet the 24" PSU, 250W works for both 2007 & 2008.
As for why these are different mostly its Wattage as Intel altered the power requirement for the chips over time.
The newer Thin Series from 2012 onward are also a bit different!
The Late 2012/Early 2013 21.5" PSU 185W is different from Late 2013/14/15 21.5" PSU 185W and the 2017/19 21.5" PSU 185W is different again! In all three cases the mechanicals are different.
The Late 2012 27” PSU, 300W, is different from the 2013/14 & Mid 2015, and the Late 2015/17 is different again and lastly the 2019/20 is also different! Apple kept moving things about mechanically.
Not sure why you want a broken PSU?? The ones I’ve listed above with links are from a good supplier which I use based in the UK. iFixit also sells the 27” 2009/10/11 iMac systems iMac Intel 27" EMC 2309, 2374, 2390 or 2429 Power Supply