sozial
social
Relates to society, people living together, and the structures of a community.
Arbeitslosigkeit ist ein großes soziales Problem.
Unemployment is a major social problem.

social
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social
Relates to society, people living together, and the structures of a community.
Arbeitslosigkeit ist ein großes soziales Problem.
Unemployment is a major social problem.

The word 'sozial' (social) is the basis for many important nouns in German that relate to society. If you see 'sozial-' at the beginning of a word, it often has to do with community, the state, or help for people.
Der Sozialstaat sichert die Bürger bei Krankheit und Arbeitslosigkeit ab.
The welfare state protects citizens in cases of illness and unemployment.
In the context of society and politics, 'sozial' (social) is often used in fixed terms. Common combinations are 'soziale Gerechtigkeit' (social justice), 'soziale Medien' (social media), 'soziales Netzwerk' (social network), and 'soziale Marktwirtschaft' (social market economy).
Soziale Netzwerke haben die Art, wie wir kommunizieren, stark verändert.
Social networks have greatly changed the way we communicate.
When it is about help and commitment to others, you will find 'sozial' (social) in combinations such as 'soziales Engagement' (social commitment), 'ein freiwilliges soziales Jahr' (a voluntary social year), or 'eine soziale Einrichtung' (a social institution).
Viele junge Leute machen nach der Schule ein freiwilliges soziales Jahr.
Many young people do a voluntary social year after school.
When 'sozial' (social/sociable) describes a person, it means that this person likes being around people and easily makes contacts. In this case, it is usually used with the verb 'sein' (to be).
Er ist ein sehr sozialer Typ und immer für einen Spaß zu haben.
He is a very sociable guy and is always up for a laugh.
social / societal
'sozial' and 'gesellschaftlich' can both mean that something has to do with society and how people live together. In this sense, they are often very similar. 'gesellschaftlich' fits especially well when talking about developments, rules, problems, or changes in society as a whole. 'sozial' is somewhat broader and can also have other meanings, for example help for people or sociability. When it is only about the structure of a society and how people live together, both words are often possible.

Soziale Fragen spielen bei der Planung neuer Wohnungen eine große Rolle.
Social issues play a major role in the planning of new housing.
Gesellschaftliche Veränderungen merkt man oft zuerst in den Schulen und Familien.
Societal changes are often noticed first in schools and families.