^ This. There are A and B standards, and each standard has its own crossover. But there is also a crossover between A and B standards, which is typically what is used when referring to crossover cables.
It's not for going between 568A and B, it's just terminated that way. What is flipped is the transmit and receive pins. It's used in equipment that can't auto-mdix, if you need to connect two ports or two interfaces. Like interface on a NIC with a router, or ports on two switches/hubs.
Ahhh that brings back memories.
hilariously one from 2015 when a buddy and mine were abroad and didn't have internet for a good month.
Raven shield co-op with no hardware
(If you didnt know, gigabit+ ethernet adaptors dont require these as they automatically make normal cables work as crossover, this was for 10/100 adaptors)