Brave New Words: The Oxford Dictionary of Science Fiction (edited by Jeff Prucher) defines "ultradrive" as follows:
Ultradrive n. a space drive that enables spaceships to travel faster than the speed of light. Compare HYPERDRIVE, OVERDRIVE.
In general, the term "ultradrive" may be used in science fiction for any FTL drive. Any idea that an ultradrive is an improvement on, or an alternative to, some other form of FTL propulsion, will be peculiar to a particular work or writer.
The earliest citation for "ultradrive" in Brave New Words is from Poul Anderson's novelette "Tiger by the Tail" in Planet Stories, January 1951, available at the Internet Archive:
Captain Flandry opened his eyes and saw a metal ceiling. Simultaneously, he grew aware of the thrum and quiver which meant he was aboard a spaceship running on ultra[-]drive.
It is not clear whether the word "ultradrive" was meant to be hyphenated or not, since the hyphen occurs at a line break.
Brave New Words does not record any uses of "ultradrive" between Randall Garrett's 1954 "Time Fuze" and Vernor Vinge's 1992 A Fire Upon the Deep, but that probably just means nobody has looked very hard for one. There is a lot of interest in antedatings, not so much in interdatings. Here is one from Algis Budrys's short story "Hot Potato" in Astounding Science Fiction, July 1957, available at the Internet Archive:
Four hundred years ago, this had been Man's earliest foothold on the stars — earliest, and, as it developed, only. The passage time had been worked down from ten years to five and a half, toward the end, but that was the best they could do. They were tinkering with an ultradrive just before the Invaders hit Earth. They still were, but it was too late for the Solar System. Centaurus was
the focus of the human race today, and Earth, like the Western Roman Empire, was a jumble of ruins where the wolves prowled down out of the hills.