So thats the technical definition of an ink and a wash... As to the actual differences when you are using it; a wash acts more like a glaze. It darkens the entire model, changes the colour of it essentially. An ink does that to a degree, but it is much happier getting into the recesses and shading in deep while leaving the raised areas exactly the same as they are. It has a much stronger colour than washes so it will deepen the colour of the recesses a lot more than a wash will. It also should not be used straight from the pot like washes, it should be watered down for use.
The effect is very different. For example, the red wash looks slightly pink and shades things red a bit, a red ink can be used from the pot as a good blood effect because the colour is that strong. I found blue wash on my LM looked terrible, and had to stick with a blue ink, however, brown washes look good on the red scales.