Unified Atomic Mass Unit and Atomic Mass Unit
After Dalton, another scientist created a scale for comparing the masses of different atoms. His name was Wilhelm Ostwald. He used oxygen as the standard for his scale, and defined one unit of mass as being equivalent to one sixteenth of an oxygen atom. He called it the atomic mass unit or amu.
Later on, people discovered isotopes, and they found that different fields of science were using different samples of oxygen as their standard (some with multiple isotopes, some only one isotope).
Science is a precise field
Science is a field of knowledge that needs to be precise - you cannot define a meter as being 95cm in one part of the world and 105cm in another part of the world. Similarly, it wasn't appropriate to use different samples as the standard for a scale.
To stop the confusion of using different standards for comparing atomic masses (i.e. to bring some form of conformity), a new unit was devised - the unified atomic mass unit. As its name suggests, it presented a new standard for the sciences to use that would unify them. This new unit was defined as being one twelfth of a carbon-12 atom.
Why not just use a known sample of oxygen or hydrogen?
To simplify matters the old standards were essentially thrown out, and the path cleared for the new unit.
Units in text-books and literature
Sometimes the literature will mix up the three different units in their text. Unless specifically defined as being otherwise, you can assume that any mention of 1 dalton (Da) or 1 atomic mass unit (1 amu) is essentially the same as 1 unified atomic mass unit (or 1u) - they're just using the old terminology for the new standard unit.