Both come off the same truck, so people use the names interchangeably. They are opposite ideas. Pressure washing cleans with force. Soft washing cleans with a solution and barely any force at all. Knowing which surface gets which is the whole trade.
Soft washing, in one paragraph
The pressure is closer to a garden hose than a jet. What does the work is an eco-friendly solution that kills what is growing on the surface: the algae, mold, mildew, moss, and lichen that live on siding, stucco, roofs, and the outside of gutters. The growth dies at the root, a low pressure rinse carries it off, and the clean holds because there is nothing left to grow back from.
Pressure washing, in one paragraph
Force, saved for the surfaces that can take it: concrete, brick, and pavers. On a driveway we run a rotary surface cleaner in even, overlapping passes, so the slab comes back one uniform color instead of the zebra stripes a hand wand leaves. Even here, delicate surfaces like flagstone and sand-set pavers get the pressure they can take and not a pound more.
The rule of thumb
If it is green, black, or spreading, it is alive, and the fix is chemistry. If it is ground-in grime on hard flatwork, the fix is pressure. Roughly: walls and roofs get soft washed, slabs get pressure washed, and anything delicate gets the gentle version by default.
What the wrong choice costs
High pressure on siding pushes water up behind it, chips paint edges, and smears the living growth around, so the wall looks fine for a few weeks and comes back darker. High pressure on a roof strips the granules and voids warranties. And a gentle rinse on a gray driveway does close to nothing, because tire film and ground-in grime are not alive and do not care about chemistry.
Not sure which one your house needs? Send a photo of what you are seeing and you get a straight answer, even when the answer is that it needs both.