Confusion between inversion domains and antiphase domains is common, even in the published literature, and particularly in the case of GaAs grown on silicon.  (Similar defects form in GaN on silicon, where they are correctly identified as inversion domains).  An example is illustrated in the diagram below.
Figure 4. Highlighted area showing an inversion domain, incorrectly called an antiphase domain, in GaAs on Si.
The shaded region, B, is an example of an APD. In the figure, GaAs is grown on a misoriented surface of Si (details are not discussed here). The misorientation causes the Ga and As atoms in region B to be on opposite sites compared to the crystal matrix. The presence of the APD results in Ga sites 1, 1’, 2, 2’, 3, 3’ being bonded to Ga atoms in the APD to form an APB.
In mixed oxidation state materials like magnetite, antiphase domains and antiphase domain boundaries can occur as a result of charge-ordering even though there are no changes in atom locations. For example, the reconstructed magnetite (100) surface contains alternating Fe pairs and Fe pairs in the first subsurface layer. An antiphase domain boundary can form if two subsurface Fe pairs meet when two terraces grow together.