My guess would be that 2nd edition had wooden pawns and the later editions went fully plastic, but not positive that's what is meant by a 3rd edition. I'm only really familiar with first edition matches the 2008 release, 2nd ed matches the new printing and at some point they phased out all the wood bits.
There were already at least two printings of the '2nd edition', in the first printing there were a couple minor errors/typos in the manual and an error on one of the petri dish labels. The second printing fixed these and got a new copyright date in the manual.
I'm assuming the '3rd edition' that was added is just the newest reprint of the 2nd edition, so it might be more accurate to call it another 2nd edition printing.
I don't have the newest one, but someone did post pictures that the plastic purple cubes are now seamless which would be one change from earlier 2nd edition printings. I don't recall offhand if there were still any typos in the manual that would need to be fixes, but maybe there were some changes, and maybe the copyright date was updated.