Albus Dumbledore: " Draco. Years ago, I knew a boy, who made all the wrong choices. Please, let me help you."
Draco Malfoy: " I don't want your help! Don't you see?! I have to do this! I have to kill you... or he's gonna kill me! "
— Draco Malfoy trying to kill Dumbledore
Does he say the same in the book? And secondly, who is mentioned in the quote? Is he thinking of Tom Riddle, Grindelwald, Lucius Malfoy, Severus Snape, himself etc.?
While the dialogue in the book (Half-Blood Prince, chapter The lightning-struck tower) is generally similar, Dumbledore does not speak of “a boy who made all the wrong choices” there. Here is the relevant part; I highlighted the sentences directly corresponding to the film dialogue in bold:
‘So let us discuss your options, Draco.’
‘My options!’ said Malfoy loudly. ‘I’m standing here with a wand – I’m about to kill you –’
‘My dear boy, let us have no more pretence about that. If you were going to kill me, you would have done it when you first Disarmed me, you would not have stopped for this pleasant chat about ways and means.’
‘I haven’t got any options!’ said Malfoy, and he was suddenly as white as Dumbledore. ‘I’ve got to do it! He’ll kill me! He’ll kill my whole family!‘
‘I appreciate the difficulty of your position,’ said Dumbledore. (…) ‘I can help you, Draco.’
‘No, you can’t,’ said Malfoy, his wand hand shaking very badly indeed. ‘Nobody can. He told me to do it or he’ll kill me. I’ve got no choice.’
‘Come over to the right side, Draco, and we can hide you more completely than you can possibly imagine. (…) come over to the right side, Draco … you are not a killer …’
Malfoy stared at Dumbledore.
So the line about the boy Dumbledore used to know is probably by Steve Kloves, who wrote the screenplay for all the films except Order of the Phoenix.
Now for the question who film-Dumbledore was referring to. There are already answers arguing that it definitely was Tom Riddle, it definitely was Dumbledore himself, and it definitely was either Tom Riddle or Grindelwald; from this, I am confident to state that the reference is ambiguous and giving an answer with certainty is impossible.
Still, I can speculate about some candidates. To me “all the wrong choices” sounds like a kind of slippery slope where someone repeatedly makes bad decisions that go counter to his actual goal. This would fit very well with Snape, who – in spite of his deep love to Lily – made a number of choices that increasingly estranged her. It would also fit with Dumbledore, who strived for “the Greater Good”. However, it does not at all fit with Tom Riddle, who set himself evil goals once, then mostly made the right choices (from his point of view), consistent with his goals.
Dumbledore is speaking about Tom Riddle to Draco. There is no direct quote verifying this, but Tom Riddle is really the only character who fits the characteristics of whom Dumbledore speaks.
In Chamber of Secrets, Tom Riddle comes close to admitting to what Dumbledore is referring to in the quote to Draco, while he was talking with Harry in the Chamber of Secrets:
‘I bet Dumbledore saw right through you,’ said Harry, his teeth gritted.
‘Well, he certainly kept an annoyingly close watch on me after Hagrid was expelled,’ said Riddle carelessly. ‘
Chamber of Secrets - Chapter eighteen, The Heir of Slytherin - Page 230 - Bloomsbury
I think Dumbledore is talking about himself.
Dumbledore associated with Grindelwald “for the greater good”:
Grindelwald. And at last, my brother had an equal to talk to someone just as bright and talented he was. And looking after Ariana took a backseat then, while they were hatching all their plans for a new Wizarding order and looking for Hallows, and whatever else it was they were so interested in. Grand plans for the benefit of all Wizardkind, and if one young girl neglected, what did that matter, when Albus was working for the greater good?
But that lead to her death:
And how did the mysterious Ariana die? Was she the inadvertent victim of some Dark rite? Did she stumble across something she ought not to have done, as the two young men sat practicing for their attempt at glory and domination? Is it possible that Ariana Dumbledore was the first person to die “for the greater good”?
Dumbledore always remorsed that and felt responsible for it:
Ariana's death, and Albus's feeling of personal responsibility for it [...], left their mark upon him forevermore.
So Dumbledore considers himself a killer, and doesn't want Draco to become one too.
(I thought you were asking who Draco was talking about, so here that is) Out of the people you mention: Lucius Malfoy would rather kiss a tarantula than kill his son, Severus Snape took an Unbreakable Vow to help Malfoy, and Grindelwald is in Nurmengard. Voldemort seems the only logical choice, as he is the one who entrusted Malfoy with this job.
(Here's one for Dumblydorr): Riddle and Grindelwald alone out of those you mention work in this context. Ithink that this quote was meant to be ambiguous. Of course, at the time Harry probably assumed Voldemort, since he didn't know about Dumbledore's history with Grindelwald, but I anrrowed it down to two; you do the rest.
And no, this quote is not in the books. A close one that I could find is:
"Well, then, you must get on and do it, my dear boy,” said Dumbledore softly.
There was silence. Harry stood imprisoned within his own in- visible, paralyzed body, staring at the two of them, his ears strain- ing to hear sounds of the Death Eaters’ distant fight, and in front of him, Draco Malfoy did nothing but stare at Albus Dumbledore, who, incredibly, smiled.
"Draco, Draco, you are not a killer.”
“How do you know?” said Malfoy at once. He seemed to realize how childish the words had sounded; Harry saw him flush in the Mark’s greenish light.
“You don’t know what I’m capable of,” said Malfoy more forcefully. “You don’t know what I’ve done!”
“Oh yes, I do,” said Dumbledore mildly.
The final and most worthy reason, however, is, of course, Because the films are nonsense
To answer your first question (as the other answers only seem to address the interpretation of the movie quote): No, the book is different.
This is the text up-to and including the reason for Malfoy to act:
‘There is little time, one way or another,’ said Dumbledore. ‘So let us discuss your options, Draco.’
‘My options!’ said Malfoy loudly. ‘I’m standing here with a wand – I’m about to kill you –’
‘My dear boy, let us have no more pretence about that. If you were going to kill me, you would have done it when you first Disarmed me, you would not have stopped for this pleasant chat about ways and means.’
‘I haven’t got any options!’ said Malfoy, and he was suddenly as white as Dumbledore. ‘I’ve got to do it! He’ll kill me! He’ll kill my whole family!’
Apart from that, in that chapter (27, The Lightning-Struck Tower) Dumbledore only uses the word boy once more, and then in reference to Malfoy: ‘Well, then, you must get on and do it, my dear boy,’ said Dumbledore softly.. The word choices doesn't appear in the entire book.
The difficulty determining who the film-script might be referring to, could have to do with this reference not existing in the books.
