Nuclear missiles were a type of nuclear weapon.
In the 1970s, an American space station fired nuclear missiles at a Zeron spacecraft, failing to destroy it. The Third Doctor used the missiles' warheads to construct a bomb which could and did destroy the Zerons and their ship. (COMIC: The Enemy from Nowhere)
When nuclear missiles were launched on an alternate Earth, the Seventh Doctor materialised the TARDIS around the whole planet so that the temporal grace would prevent the missiles from exploding. (PROSE: Blood Heat)
In 1983, the Ice Warrior Skaldak was found frozen underneath the North Pole by a Soviet submarine. He awoke and threatened to launch a nuclear missile, allowing the superpowers to launch missiles at one another, causing mutually assured destruction. He was stopped once an Ice Warrior ship rescued him. (TV: Cold War)