In image A, we can clearly see a distinguishable boundary between oil and water. Furthermore, when I move from point A to point B to point C, we can intuitively understand that there will be no change (assuming uniformity) in physical properties when I move from point A to B where there will be an abrupt change in properties like density, refractive index etc. And when I move from B to C, there will again be no change.
A region of uniform physical properties and chemical composition with an often distinguishable boundary is called aphase.
In the solution in image B, we can find no boundary within the solution and the physical properties are uniform throughout.
If you want to know more about the boundary, go refer the video again.