If you want to get some understanding of socialism from an anarchist perspective I can't recommend enough either Anark for videos, or An Anarchist FAQ for text. Both of these also include a lot of explanation of where anarchism fundamentally differs from Authoritarian Socialists (AKA Marxist-Leninists) and Libertarian Capitalists (AKA "Anarcho"-Capitalists)
Socialism
Rules TBD.
I think the Tankie Triad term is more about linking certain people with support for authoritarian policy, rather than socialism as a whole. There are a ton of people across Lemmy instances that think of themselves as socialist and reject authoritarianism. They might use the term "tankies" to distinguish between themselves and those socialists who might support "using tanks" to suppress dissent. So the distinction you see some draw could be more about that instead of socialists vs non-socialists. People on one side tend to paint socialists as liberals, and people in the other side tend to paint socialists as tankies. Reactionary comments are easy to make and aren't useful but people make them anyway for a myriad of understandable reasons so that's that. ๐ฅน
That's my understanding on this part of the issue so far.
One small observation - everything I know about socialism I learned years and years before the term "tankies" existed, so I'm pretty sure they aren't fundamental to socialism.
Secondly, we don't live in a binary world. Countries that are primarily capitalist still do many things collectively - fire departments for example. The argument is always over which aspects of life to socialize and which to leave in private hands.