On a functional level on the user end, it's identical to a normal ban. Functionally, one is triggered via the warn system, and another is triggered by the ban feature.
The warning system is where users collect warning points. When a user triggers 100%+ points, they will be issued a ban, but you can be issued a ban without collecting 100% first. That's what the ban feature is for.
However the reason why you might've gotten the previous banner is sometimes mods will use the traditional ban feature to issue some self bans just because the timer is a bit easier to use on there and it gives users a date/time. When a warning is set to expire via the warn system, a user doesn't see the timer on their end because they don't see the warning history or warning info that isn't sent in a PM.