I think this is correct. While on a purely technical sense they mean pretty much the same thing, I think in common usage "cleansing" is used more for more serious or exacting things (along with what Heartbroker said above), like a doctor sterilizing an object or a wound for example. Even then you could use the would "clean" in that situation also and nobody would think it was weird or notice it.
When in doubt I would just go with clean as it would work in nearly all common situations.
i feel very little need to participate in society, i find most of what it offers meaningless and trivial, yet i find myself compelled by forces outside myself to be a part of it