I am a part-timer, mainly staying in developed campgrounds these days. Grey water is a headache, and I also try to minimize it (but probably not as effectively as Mr. Noodly, et al.). Everything we use is captured and disposed of in designated facilities (of which there are few near BLM/Forest Service dispersed areas). I have a small sink inside for quick sponge baths and tooth brushing. It drains into an empty cat litter jug, which is easy to empty. Outside hair washing/showers are done over a plastic tote, then poured or pumped into a jug for dumping. I used to stand in a masonry tub when showering, which I have now replaced with a folding dog pool. So far, I have not actually used the pool, but is is easy to drain a small amount of water into a container from either of these. Spraying is fine, but I like to hot-water-wash my eating utensils and cups. I do this in a plastic bowl with a pour spout and lid. Doesn't take much water if you wipe first. Personally, I don't think soap is always necessary. The dishwater is then poured into the sink, or sometimes added to a pee jug for later disposal. (Well...)
Most of the places I am in lately see heavy use and are close to bodies of water. It doesn't take much detritus to cause problems and encourage pests, so I really strive not to make it worse. In other settings, I would have no problem scattering small amounts of essentially clean water.