Well there definitely is a terminology issue here, and yes it is a South Africanism, mostly because data and bandwidth (yes both) cost so much here.
Basically and by law, capping refers to the termination of service when a specific threshold is reached. The law defined this and made it unlawful for ISP's to do, expecially on local. This does not then mean that you can download as much as you want for free, simply that they cannot terminate your service.
These new cheap "uncapped" services therefore do relate to the "lawful" (should that be awful) definition, in that they do not terminate your service, they simply bill the cr*p out of you.
Other "uncapped" and "data unlimited" services, the more expensive ones where you don't pay for overusage (though if they feel you broke the EULA, they might) will still start to limit your usage after an allocated transfer rate. This is called a rolling throttle, which occurs every 10 days and aggregates your usage over the last 10 days to determine by how much / whether to throttle your service, usually to around 128Kbps (Even on a 4 Mbps line!)
There is no feasability for true uncapped, unbilled, unlimited, unthrottled, unshaped packages in this country, and even in the US now, ISP have begun introducing caps, albeit extremely high ones, just to crack down on those really sick bandwidth abusers (200 GB data a month!).