It's impossible to definitively say.
The film was only intended as a one off movie, with three films being created out of it. It was certainly suggested by the film makers that in the second film Eastwood was playing the same character as in the first.
Robert C. Cumbrow discussed this ongoing questions in "The Films of Sergio Leone", commenting:
We assume from the beginning that Eastwood, in For a Few Dollars
More, is playing the same character he had played in A Fistful of
Dollars. In fact, the advertising campaign for the film encouraged us
to do so ("The Man with No Name is Back and the Man in Black Is
Waiting for Him!"). But jarring points signal character
dissimilarities. Eastwood's called "Manco" in the Italian prints (and
in at least one American print), he's more mercenary than he was in
the previous film, and he talks about wanting to use his money to (get
this) retire! His character's morality is even more pragmatic than it
had been in A Fistful of Dollars, where at least he does what he
does in order to protect the innocent. There is a certain bond of
honor with Colonel Mortimer; but most of what Eastwood's Manco does in
the film is consistent with the bounty-killer amorality ascribed to
him from the onset.
Yet poncho and cigar, stubble and squint persist through all three
Eastwood/Leone films. If the characters portrayed by Eastwood are not
supposed to be the same man, it is at least fair to treat them as
variations on a theme. What theme? Screen Western heroism stripped of
all pretension and motivation and forced to look inward to see a
truth: Show me a hero and I'll show you a villain with good excuses.
There's good and bad (and ugly) in all of us, and Eastwood was the key
player Leone used to mold traditional Western-movie heroism into
something with darker roots - it not Hell, then at least purgatory.
It must be noted however that The Good, The Bad and The Ugly was the final film released and if applying logic to the trilogy, as it is set during the Civil War, it would only make sense to be a prequel.
If we assume it is a prequel, then almost the only piece of evidence which could be used to suggest the film features the three characters is that Eastwood slowly builds up his "costume" for the first two films throughout The Good, The Bad and The Ugly, finally completing the look when he dons the poncho near the end of the film.
So in conclusion I would argue this:
It was meant to be a one off film. They created a second and played on Eastwood being the same type of character, without really caring too much if he was the same character (hence the character differences). Then for the final film, they chose to make it as a prequel and did intend for the character to be the same as in the first film.
As with @Napoleon Wilson's answer, this is all just conjecture, but I doubt we'll find anything better on the topic.