Historically the Soft incandescent bulbs had a more diffused light, while the not-so-soft bulbs had a more visible filament and harsher light quality with more direct glare from the bulb.

The white coating on the glass that provided the softer look also tended to absorb some of the light so a soft bulb would put out fewer lumens than a non-soft bulb from the same manufacturer of the same wattage.

Perhaps in the LED world this still means a softer overall appearance to the illuminated bulb, not a reference to the color temperature or CRI index.

Outside I still prefer the warm white color over the daylight bulbs. At night I find the daylight color to be quite cold looking and rather blue. The warm white color seems more welcoming at night, without looking too yellow.