Newly offered for 2010 the C59H is a significant step up from the A58H described previously. Listing for just $10 more than the A58H, I suspect that many people will find the C59H worth the added cost.
With respect to the A580IP and S675IP the C59H is being offered only as an optional expansion handset. You must have one of the two IP capable systems, then you can add the C59H if desired.
Within the Gigaset SIP/DECT product range the IP enabled base systems are clearly indicated with an “IP” model designation. You may also see Gigaset offering a model C590, if not in the US at least in other parts of the world. The C590 is a complete system comprised of a DECT base and one C59H handset. However, the DECT base in question is not IP capable. It does not have a network connector, only the analog line interface.