Ofc, for example 5,56 mm bullet can kill large wild pig etc.
While there are thing called stopping power.
It was well researched during period like 1900-1945 and was reason why caliber for handguns used by police and agents & military caliber had been increased.
Soviets had used 7,62 mm Nagant and 7,62 ( 7,63 ) Mauser and TT.
After WW2 they had opted to develop 9*18 mm cartridge and PM & APS pistols.
While of course Mauser and TT with 7,62*25 cartridge had good penteration and to kill from these someone from 60 meters distance was possible.
Germans too had Mauser with 7,62*25, pistols chambered with 32 APC and these with 38 APC ( 9*17 ) and Para ( 9*19 ).
Later decided that 9*17 and 9*19 are more effective for 1 shot fast stoppage.
U.S in end of 1930 ies too had reccomended to use at least 38 cal revolvers or pistols chambered with 9*17 or 9*19 rounds or something in larger calibers than these.
Not all shots are ideally precise and the lesser distance animal will walk after is get shot, the better.
In some hunters circles the more efforts from mates you will need to collect animal from bushes somewhere, the more reward you should gave them for their efforts.