There are some caveats with Hayt, but in general, the ghola process is cloning. As little as a single cell is used to regrow a human being in an axlotl tank, which is actually
a Tleixu female.
This is a closely guarded secret. What you seem to be referring is this:
"We are pleased to accept your credentials," Paul said. "Explain the gift."
Edric rolled in the tank, bringing his attention to bear on the ghola. "This
is a man called Hayt," he said, spelling the name. "According to our
investigators, he has a most curious history. He was killed here on Arrakis . . . a grievous head-wound which required many months of regrowth. (Dune Messiah)
As I said, the axlotl tanks are a closely held secret by the Tleilaxu. Even the Bene Gesserit did not understand the whole secret behind them thousands of years later. It seems likely the Guild is simply misinformed as to how the ghola process works.
Gholas do not, by default, have the memories of the original.
"I know nothing of my past for sure, my Lord. It was explained that I can
have no memory of my former life. All that remains from before is the pattern
set by the genes. There are, however, niches into which once familiar things may fit. There are voices, places, foods, faces, sounds, actions -- a sword in my hand, the controls of a 'thopter . . . "
(Hay, Dune Messiah)
However, these memories can be awakened through an emotionally traumatic trigger event. This is not because the ghola is a regeneration of the original body, but because, as suggested in the above quote, memories in Dune are encoded on a genetic level - this is how taking enough spice, for the initiated, can awaken all their ancestral memories. (Later, of course, somehow a ghola-of-gholas is able to access memories he shouldn't have, suggesting that there is indeed some kind of supernatural aspect to it.)
Hayt later, in Children of Dune, makes this same comparison:
Computation: A reflected Lady Jessica lived out a pseudo-life in Alia's
awareness. He saw this as he saw the reflected pre-ghola Duncan Idaho which
remained a constant in his own awareness. Alia had this awareness by being one of the pre-born. He had it out of the Tleilaxu regeneration tanks. (Children of Dune)
Of course, you can see here that Hayt (apparently) wrongly believes the axlotl tanks are regeneration tanks. To be fair, it's possible that at this time, or in Duncan's particular case, they were able to use an entire corpse as the start of the process, but elsewhere we are shown that ghola go through childhood and age like normal people. (There is a bit of a timeline problem in the Hayt case if he was cloned from a few cells, because Hayt was evidently not twelve. Out-of-story, it seems that Frank Herbert hadn't decided how the ghola process was to really work.) Jessica believes the same thing:
But the Tleilaxu had bought his body from the Sardaukar and, in
their regeneration vats, they had grown a zombie-katrundo: the flesh of Duncan Idaho, but none of his conscious memories. He'd been trained as a mentat and sent as a gift, a human computer for Paul, a fine tool equipped with a hypnotic compulsion to slay his owner. The flesh of Duncan Idaho had resisted that compulsion and, in the intolerable stress, his cellular past had come back to him.
To be fair, it's possible that - somehow - if the Tleilaxu have an entire corpse, they can begin the process from there, rather than from scratch. That's never how it is portrayed or referenced after Hayt, however. Or, that the ghola process changed through time. 3500 years later, it was clear that only a few cells were necessary.
To find himself living when he knew he had died, that was proof enough. The Tleilaxu had taken cells from his dead flesh and they had grown a bud in one of their axlotl tanks. That bud had become this body in a process which had made him feel at first an alien in his own flesh. (God Emperor of Dune)
More than one could exist at a time:
At the last instant, the Duncan had tried to throw the explosive to one side, but the material in it had been unstable and it had gone off too soon. The Duncan had died. Ahh, well-the Tleilaxu always had another in their axlotl tanks. (God Emperor of Dune)
A ghola had a ghola-childhood:
He could not remember the axlotl tanks where his cells had grown into an infant. His first memories were of Geasa picking him up from his cradle, the alert interest in those adult eyes that had so soon faded into wary lidding. (Heretics of Dune)
That said, the characters in Dune do differentiate betweena ghola and a clone.
"At Bene Gesserit behest," Schwangyu said, "the Tleilaxu have made a significant alteration in the present Idaho series. His nerve-muscle system has been modernized."
"Without changing the original persona?" Teg fed the question to her blandly, wondering how far she would go in revelation.
"He is a ghola, not a clone!
(Heretics of Dune)
One presumes, if Schwangyu is not simply saying that altering the individual makes them not-a-clone, that clones do not, for some reason, retain the original persona.