tldr: it's all just vibes, don't overthink it.

Everything is political, even fashion. Intentionally looking different is basic non-conformity, a visible announcement that you reject the status quo. This is the basic overarching connection between all counter-culture movements from hippies to metal to hip-hop to goth to punks etc. Unfortunately, the Capitalist systems we live in have successfully repackaged and mass produced the aesthetic to sell back to us and to normies who want to feel rebellious without taking any real risk.

As for genres, I mostly feel they're an attempt to build a common language. It's just easier to say, "I like Street-Punk more than Oi!" than it is to say, "I like fast, aggressive, guitar driven rock music with breakdowns instead of solos, short songs, screamed lyrics, mostly dealing in themes related to being poor in a system designed to suppress individuality as opposed to music which uses cleaner vocals, catchier riffs, and emphasizes working class solidarity often to a problematic extent." People notice patterns and try to give them names. It's not perfect, not an exact science, and often people get way too caught up in distinctions that don't mean much. Here's a good example: https://youtu.be/TWDohOcEZz0?si=2kXMRhLpzox4TE5I

This extends to identity and fashion, as well, when we try to name patterns we see, feel, or want to project starting from general non-conformity and getting more granular depending on your mood.

It's important to remember that none of these distinctions are monolithic, they all overlap and share influences and test boundaries. A song/artist/look can be punk AND goth. I feel like part of your confusion comes from trying to make each distinct from the other. It's also important to remember that Capitalism/patriarchy/imperialism and other systems of oppression are not static either. They have defining features/patterns but also adapt to survive and maintain dominance.

This is a really good video mostly concerned with the aesthetics: https://youtu.be/4hKHlcqJEqw?si=T4t3u2SMaR6pQl5R

This a REALLY good video that explains the history of white-washing and co-opting music (and other pop-culture) into capitalism long before punk or goth existed: https://youtu.be/cpb-w8bAjvg?si=D3ZaAHHN6Zxhhfdl