I'm not sure power structure is inherently part of the definition. There's a certain kind of communism that supports the vanguard party, General Secretary, etc.

I'm not sure power structure is inherently part of the definition. There's a certain kind of communism that supports the vanguard party, General Secretary, etc. (the Soviet approach). POUM had a lot of anarcho-communists, and more recently council communism also supports decentralized power. There's a lot of gray area in the terminology. I think the terms are more different now than they used to be, however. Many libertarian socialists who might've used the term "communism" prior to the 1930s are more likely to call themselves something else today, to avoid being mistaken for Leninists or Stalinists. But it's pretty hard to call POUM "social democratic" or even "democratic socialist" either. By modern standards they are far too radical-left to fit into a "respectable" socialist or social-democratic party. Could you imagine them standing for Labour, or the Parti Socialiste or SPD? Waving a red flag and declaring that the time is ripe for the socialist revolution...