all the words tend to be interchangable.
for instance there are many products that will only brighten and even out skin tone but marketers will use terms like lightening to make it sound like its a drastic process. "whitening is also used to suggest a product will also have drastic lightening properties. bleaching is used because when one thinks of bleach you think of white dingy cloths becoming bright and white. also bleaches removes stains and color. there are bleaches that will actually destroy pigments in the skin and make the skin "white". Hydrogen Peroxide is a populare one and works instantly. most skin lighteners will actually just reduce the production of pigments by reducing the formation of an enzyme responsible for dark pigments.
it doesnt matter what wording you see on a product. all that matters is whats in it and what the concentration of the active ingredient(s). some ingredients tend to brighten/even skin tone which isnt that drastic. so that would be good for correcting hyperpigmentation and melesma. other products contain stronger lightening agents that will actually stop the production of pigment in normal melanocites which will actually lighten the overall complexion of a person.
as for soaps being significant, the answer is simple, NO!!!. soaps with so called "skin lighteners" in them are a waste of money. the water you use to make a lather will dilute the actives in the soap and you will end up rinsing the soap off before it gets a chance to be absorbed by the skin. soaps are for cleaning skin so dont waste type with buying anything special for skin lightening. stick with acid peels, retinols, enzyme peels, microdermabrasion... to help lift off dead skin (which allows creams to work better and quickens the results) and then use a topical cream with well known and safe actives.