It is easy to get confused because the words have more than one use depending on the context.
In common language, "dispersion" refers to a spreading out, while scattering a special way that something may get spread out.
i.e. you may disperse seeds over a field by scattering them from your hand.
Light may be scattered from an object so it is dispersed over a screen.
Be careful though: "scattering" and "dispersion" are also technical terms in physics.
"scattering" is a particular process where incoming radiation, like light, is sent off again in random directions.
"dispersion" refers to the way a pulse (of light, say) spreads out in the direction of travel.
The technical use of "scatter" is very similar to the common one, but the technical use for "dispersion" is quite different... so we have to talk about scattered light being distributed over a screen rather than dispersed.