They are not TST-affiliated, more like an old style LaVeyan group.
The Satanic org I'm a member of also have a Chilean Order and I know the two orgs have talked but their LaVeyan-ism (i.e. libertarian/Ayn Rand type of Objectivism) doesn't really align with us.
The worst thing about Satanism is that you have to do a lot of research to know whether that new group are nice goths for social justice or some kind of neo-Nazi paedophile ring or something. It’s like extreme metal bands.
Anton LaVey’s Church of Satan: started out as a reaction against the “peace and love” vibe of the late 60s. Influenced by Ayn Rand and sophomoric readings of Nietzsche. The old-school edgelord assholes, though these days, the mainstream political right has largely caught up with them.
The Satanic Temple: either Goths for Social Justice or a performance-art project (“what if Satanism, but nice?” and “what if we used freedom of religion against the fundies?”). Very much against racism/sexism/the Religious Right, for LGBT rights, etc. There has been some criticism of the founders and whether they’re Milkshake Duck, though they largely introduced the Nice Satanism meme.
Global Order of Satan: largely UK/European network, influenced by TST but critical of the organisation. Generally good guys. Strongly involved in social-justice activism. They have affiliates, such as Sataniska Samfundet in Sweden and GOS Polska in Poland.
Order of Nine Angles: neo-Nazi edgelords who relish being evil. Very much not the good guys.
Yeah, we broke away from TST in around 2018. Too centralised, too controlling, with concerning owners. We also have a couple of US Orders these days (Steel City in Pittsburgh and House of Heretics in Seattle).