They're different terms. Both are nouns. I think -ing is added in order to differentiate it from social distance (sociology).
Social distancing (noun):
the practice of maintaining a greater than usual physical distance from other people or of avoiding direct contact with people or objects in public places during the outbreak of a contagious disease in order to minimize exposure and reduce the transmission of infection. (M-W)
Social distancing, or physical distancing, is a set of non-pharmaceutical interventions or measures taken to prevent the spread of a contagious disease by maintaining a physical distance between people and reducing the number of times people come into close contact with each other.It involves keeping a distance of six feet or two meters from others and avoiding gathering together in large groups. (Wikipedia)
Social distance (noun):
the extent to which individuals or groups are removed from or excluded from participating in one another's lives.
Social distance describes the distance between different groups in society, such as social class, race/ethnicity, gender or sexuality. Different groups mix less than members of the same group. It is the measure of nearness or intimacy that an individual or group feels towards another individual or group in a social network or the level of trust one group has for another and the extent of perceived likeness of beliefs.
Robert E. Park defined social distance as "an attempt to reduce to something like measurable terms the grade and degrees of understanding and intimacy which characterizes personal and social relations generally". (Wikipedia)