The KC135 has a different airframe to the B707.
designations for actual 707s include:
-137 (used as Air Force One until replaced by B747/VC-25), I think the veep usually uses one these days if any are still in service
E-3 Sentry (AWACS)
-18 Range Instrumentation & cruise missle control (originally exAA 707-320Bs, much reworked of course)
designation is E-6 Mercury (submarine comms & airborne command post)