But why didn't Sabertooth remember? Did they both have memory loss?
In the comics they do, yes. Weapon X put all sorts of weird memory implants into their agents, and did a bunch of tampering with their heads to the point that they have memory loss, false memories, etc.
Wolverine and Sabretooth remember that they have some kind of past together (in the comics), and even remember some vague shared themes (such as Sabretooth killing Silver Fox- which turned out to be an implant), but the only ones who have seemingly ever worked completely through their memory tampering are John Wraith and Maverick- and even that is questionable, as Maverick once made a comment that he did sort through them, but in his later series we see that he hadn't completely. (Note that Wolverine- due to the Scarlet Witch's tampering in House of M has seemingly regained all his memories in the current MU.)
Presumably, the movie is just taking the stance that neither Wolvie nor Sabretooth even have any recollection of one another, as opposed to the kinda/sorta that they have in the comics.
(Spoilers removed in the next section because the movie has been out for 5 years now, and I don't think it's really spoiler worthy at this point. If anyone really has problems, I will certainly put them back in):
Edit: There's also the bit in the second movie where Striker says something along the lines of, "I thought you were one of a kind, but turns out not," and leaves Logan to fight his mind-controlled long-nailed equivalent. If Sabertooth had ever been considered for the program I would've through Striker would have made a slightly different comment. The way he said it made it sound like Logan was the only possible candidate for the procedure at the time.
I recall the quote- it came around the time he sicced Deathstrike on Logan (and what a wasted character that was in the movie). Still, the comment's vague enough that it could have been referring to pretty much anything. Maybe it was Logan's moral character or martial ability ("The best he is at what he does") that Stryker was referring to, rather than the similarities of the powersets of Logan and Creed. More likely they hadn't yet considered involving Sabretooth in the backstory of Weapon X in the movies at that point (which certainly seems to be the case regarding Sabes in the first movie). Most of the villains in X1-3 were just 2 dimensional constructs who existed only to serve as foils to the heroes.