There isn't a connection, one network (TWIT) is fronted and owned by Leo Laporte, the other (This Week In) by Jason Calacanis.
Laporte doesn't seem to like how Calacanis has diluted the TWIT brand by launching a similar sounding network, so Calacanis is essentially banned from appearing on Laporte's network.
Not really a fan of either though. These days, TWIT seems to focus on shows that are opinion heavy, rather than content heavy, while Calacanis' podcasts feel a bit too "pie in the sky".
There is no connection between thisweekin.com and TWIT, other than they share a common naming convention.
For the record, I got permission from Leo to buy and use the domain. however, since we launch 17 shows in under six months he is a little upset with me.
