gesellschaftlich
societal
Relating to society as a whole, that is, the structure of society and the way people live together.
Armut ist ein großes gesellschaftliches Problem in vielen Ländern.
Poverty is a major societal problem in many countries.

social / societal
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societal
Relating to society as a whole, that is, the structure of society and the way people live together.
Armut ist ein großes gesellschaftliches Problem in vielen Ländern.
Poverty is a major societal problem in many countries.

The adjective 'gesellschaftlich' (social/societal) is derived directly from the noun 'die Gesellschaft' (society/company). It takes on its double meaning: it can refer both to society as a whole (state, people) and to a smaller group of people at an event.
Die Digitalisierung verändert unsere Gesellschaft tiefgreifend.
Digitalization is profoundly changing our society.
You can recognize the meaning from the context. If it is about large, abstract topics such as politics, economics, or culture, society as a whole is meant. If it is about parties, meetings, or people's behavior, it refers to being together with others.
Bildung ist eine wichtige gesellschaftliche Aufgabe. (Thema: Gesellschaft)
Education is an important societal task. (Topic: society)
When referring to society as a whole, 'gesellschaftlich' (societal) is often combined with abstract nouns. Typical examples are 'gesellschaftlicher Wandel' (societal change), 'gesellschaftliche Verantwortung' (social responsibility), 'gesellschaftliche Normen' (social norms), or 'gesellschaftliches Engagement' (social commitment).
Der Klimawandel erfordert einen tiefen gesellschaftlichen Wandel.
Climate change requires profound societal change.
political
'politisch' and 'gesellschaftlich' can both be used for topics that affect many people. 'politisch' fits when it is about parties, government, the state, laws, or political opinions. 'gesellschaftlich' fits more when it is about the way people live together, social groups, or changes in society. You can confuse the words because many problems are both, for example education or housing. If the state or political decisions are the focus, 'politisch' is more precise. If people's lives in society are the focus, 'gesellschaftlich' is more natural.

Einsamkeit ist ein gesellschaftliches Problem, das viele Altersgruppen betrifft.
Loneliness is a societal problem that affects many age groups.
Die politische Entscheidung über die neuen Regeln wird am Montag bekannt gegeben.
The political decision about the new rules will be announced on Monday.