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Both are the addressing formats for IP addresses.
IPV4 is presently used 32 bit addressing format. No one really thought all the 2^32 address could be used , hence limited it to 4 bytes only to realise every device which connects to internet uses a unique address -most of the 2^32 addresses have been used up. These addresses were initially divided into various classes in order to divide the address ranges being used by various groups like class A , class B et al. along with other mechanisms like subnets were introduced - people who were intuitive to foresee use up of IPV4 , percieved IPV6 which is made up of 128 bits. ie a total of 2^128 addresses can be assigned.
though this solves the basic problems , there are still changes to be done to the routing process and older versions of routing tables as such.