In U.S. mathematics, "one-to-one function" means injective (i.e., every element in the image of a mapping has a unique pullback but the image is not necessarily equal to the co-domain/range).

I can see how the wording "one-to-one" is confusing, since "one-to-one correspondence" is widely used as "bijective". Thanks for pointing this out — I'll be more careful on using "one-to-one" in the future.