Mojang has (slightly) improved its account management. With the release of Cobalt and the hosting by Mojang, they decided to create Mojang accounts, so that players didn't need a separate account for Minecraft and Cobalt. A Mojang account will handle both. However it is up to Minecraft players to change their accounts over by visiting https://account.mojang.com/
If you are not a Cobalt player, then there is really only one major advantage for having a Mojang account, rather than just a Minecraft account - it allows you to change which email address you associated with your account. Indeed, it is your email address which is your account username, not your Minecraft name. However, your Minecraft username will always be the same. Though many people have complained about this as they want to be able to rename themselves, Mojang are yet to work out how to add such a capability and not create problems for sysadmins with banlists etc.
Please note though that Minecraft players do not *have* to switch to Mojang accounts. The Minecraft accounts will still work fine by themselves.