Nintendo recently revealed that Wii Points would be called Nintendo Points, and it has since been confirmed that when you buy Nintendo Points, they can only be linked to one system (either the DSi or the Wii).
In summary, you can not use the same Nintendo Points card to download both Wii Ware and DS Ware.
To quote: Nintendo Points will be activated for the Wii or DS and not shared between them, reports [Register or Login to view links]. With the announcement of the Nintendo DSi, the company also gave word that Wii Points would be renamed Nintendo Points to include both Wii Ware and the new DS Ware.
One might have reasonably assumed the points would transfer between systems seamlessly, but that would also require Nintendo to have a unified account system in place to handle the distribution. Since it doesn't, the Points can only be linked to one system.
For example, purchase of a 2000 Nintendo Points card won't let you use 1000 for Wii and 1000 for DS, so be prepared to make a commitment of where your Points should go. More PlayStation 3 News...