IEEE 802.11 as amended by 802.11i knows of only one TKIP.
The Wi-Fi Alliance is loath to reveal that there are interoperability problems between devices sold under their original 2003 WPA brand and their 2004 and later WPA brand. They only speak of one TKIP.
I think The CWNP Program invented the terms TKIP v1 and TKIP v2 in an effort to sort out the confusion wrought by the multiple meanings assigned to "WPA".
Maybe instead we should leave IEEE's TKIP alone and instead put the monkey on WPA(2003) and WPA(2004). Because WPA is about public brands and private evolving specifications for multi vendor interoperability certification, if we look closely enough we may find a WPA(2005) and a WPA(2006).
I hope this helps. Thanks. /criss