There are two different forms of FTL transport in John W. Campbell's novelette "Forgetfulness", first published (as by "Don A. Stuart") in the June 1937 issue of Astounding Stories (available at the Internet Archive). One was used by the civilization of the "city builders" millions of years before the time of the story (set in the far future). The other is used in the story by Seun, a man of "Rhth" and a descendant of the city builders, to send an invading space fleet back home, a distance of three and a half light-years, in the blink of an eye. I consider the two methods different because the ancient city builders used great machines to power their spaceships, whereas Seun used only the power of his mind, aided by a handheld crystal of his own making; also because Seun maintains that the technology of the city builders has been "forgotten" (hence the title of the story). It seems pointless to speculate on whether the two forms of FTL use the same principles; that would be trying to compare one gobbledegook with another.
Seun of Rhth on the lost lore of the city builders:
"We have forgotten so much of the things the city builders knew, their arts and techniques," Seun explained. "They built things and labored that things might surround and protect them, so they thought. They labored generations that this city might be. They strove and thought and worked, and built fleets that sailed beyond the farthest star the clearest night reveals. They brought here their gains, their hard-won treasures--that they might build and make to protect these things.
"They were impermanent things, at best. How little is left of their five-million-year striving. We have no things today, nor any protecting of things. And we have forgotten the arts they developed to protect and understand these things. And with them, I am sorry, I have forgotten the thoughts that made the lathan [an antigravity suit] understandable."
Seun discusses the sorgan which powered the city builders' ships:
"The generator supplied the power for the city, and for the ships of the city, wherever they might be in space. In all the universe they could draw on the power of that generator, through that sorgan unit. That was the master unit; from it flowed the power of the generator, instantaneously, to any ship in all space, so long as its corresponding unit was tuned. It created a field rotating"--and the minds of his hearers refused the term—"which involves as well, time.
"In the first revolution it made, the first day it was built, it circled to the ultimate end of time and the universe, and back to the day it was built. And in all that sweep, every sorgan unit tuned to it must follow.The power that drove it died when the city was deserted, but it is still making the first revolution, which it made and completed in the first hundredth of a second it existed.
[. . .]
"Since, in its first swing, it turned to that time, and back to the day it was built, it radiated its power to the end of space and back. Anywhere, it might be drawn on, and was drawn on by the ships that sailed to other stars."
Ron Thule, a Pareethian astronomer, compares the city builders with the current inhabitants of Rhth:
"Once"--Ron Thule's voice was tense--"the city builders made atomic generators to release the energy bound in that violent twist of space called an atom. He made the sorgan to distribute its power to his clumsy shells of metal and crystal—the caves that protected him from the wild things of space.
"Seun has forgotten the atom; he thinks in terms of space. The powers of space are at his direct command. He created the crystal that brought us here from the energy of space, because it made easy a task his mind alone could have done. His people have no ships; they are anywhere in space they will without such things. Seun is not a decadent son of the city builders. His people never forgot the dream that built the city. But it was a dream of childhood, and his people were children then. Like a child with his broomstick horse, the mind alone was not enough for thought; the city builders, just as ourselves, needed something of a solid metal and crystal, to make that dream tangible.