Main difference:
BDC = SharePoint 2007
BCS = SharePoint 2010
There is no BDC anymore in SharePoint 2010 or 2013. And you can also say that BCS is an extension of BDC or newer version of BDC.
The Business Data Catalog (also known as BDC) existed in Microsoft Office SharePoint Server 2007 (MOSS, not Windows SharePoint Services) for read operations.
Business Data Connectivity (also acronym’ed BDC, though it’s now Connectivity, and it plays a very similar role) was introduced in SharePoint Foundation 2010 (also SharePoint Server 2010, of course). This BDC’s job is to provide connectivity to back-end data systems, as was the job of the BDC (Catalog) in MOSS 2007.
However, it’s much more rich.
It’s in Foundation, so its capabilities are available “for free”
It supports read/WRITE access to data.
Also check:
http://sharepointpromag.com/sharepoint/what-difference-between-bcs-and-bdc
http://social.msdn.microsoft.com/Forums/en-US/2970be39-89e3-475d-aa9c-300b5880f801/bdc-vs-bcs?forum=sharepointgeneralprevious