Is a soft-focus image just minimally out of focus?
No. A soft focus image is in focus, but exhibits a high degree of spherical aberration. Edges in the image will be relatively sharp, but will be surrounded by a kind of diffuse softness. This is often particularly visible as an ethereal glow around highlights. That's very different from the indiscriminate blur of missed focus.
This is a common property of many older portrait lenses, and some are even designed specifically to have the effect in variable amounts. See How do soft focus or defocus control rings work? for some great answers explaining this in technical detail.
You may also find How can I approximate 'soft focus' digitally? to be interesting, if only because you can see that the approach taken isn't the same as one might use to approximate out-of-focus blur.
No, it is a combination of light that is in focus and light that is out of focus (or otherwise blurred). An image that is just out of focus doesn't get that dreamy look, it just lacks detail.
I had a Canon 1000 camera that had a soft-focus function. It would take a double exposure, one in focus and then one out of focus.
A soft focus filter (both optical and digital ones) works in pretty much the same way, just that it uses the same image for both exposures, not two images taken after each other.
We let T-Max the cat demonstrate:
(The middle image is blurred using Gaussian blur with a radius of 2.0, then one image is just overlayed on the other with an opacity of 50%. Different settings can be used depending on taste and what the original image looks like.)