Simply put, Kh-55 and Kh-555 use basically the same rocket, but with a different payload.

Bullshit. :) Kh-55 is basic variant, Kh-555 is Kh-55 with additional features including radar, RF, IR and satellite targeting along with more precise variant of basic inertial targeting system. Warhead compartement is the same, both variants could be fitted with nuclear warhead.

Traditional explosives only variant was named Kh-65 designed for targeting ships, but it appeared only on exibitions and hardly was ever produced.

Simply put, Kh-55 and Kh-555 use basically the same rocket, but with a different payload.

Bullshit. :) Kh-55 is basic variant, Kh-555 is Kh-55 with additional features including radar, RF, IR and satellite targeting in addition to basic inertial targeting system. Warhead compartement is the same, both variants could be fitted with nuclear warhead.

Traditional explosives only variant was named Kh-65 designed for targeting ships, but it appeared only on exibitions and hardly was ever produced.