2chan is Futaba Channel, the famous Japanese image board from which 4chan is derived. Some of 4chan's memes are borrowed from 2chan. Affiliated with (and often confused with) the massive text-mode BBS 2channel (2ch); 2ch and Futaba share many of the same memes, as 2chan was created by 2ch posters. Thus, 2chan could be seen as the "parent" of 4chan, and 2ch as 4chan's "grandparent".
As of spring 2006, 4chan has actually surpassed 2chan in traffic, though 2ch is still larger than both of them combined.