Both TKIP and PSK use essentially the same WPA standard, just different ways of encrypting the same thing (hence WPA-PSK TKIP and WPA2-PSK AES).
PSK stands for Pre-Shared Key and depends on a passphrase to connect devices. TKIP is just the encryption protocol that the has been included in the WPA standard.
As far as your question, your device (the Captivate) is looking for both WPA/WPA2 PSK protocols.
I would recommend switching your router to WPA2 PSK AES anyway as it has shown to be more secure than the standard WPA-PSK TKIP.
Your wife might gripe, but if she's also using a cappy, then it won't matter since it's looking for both protocols - just use the same passphrase. For any other device, it takes a minute to change the settings and get everything up and running.
All that being said, your router settings might not have anything to do with the wifi problem. Before I started flashing ROMs, I had to constantly switch my WiFi off and then back on before it connected.
Hope that helps and wasn't too confusing.