Yes, project Chanology should be considered synonymous with the group Anonymous, because the group Anonymous is behind project Chanology. The Anonymous group participates in hacking activities intentionally, but they also go to great lengths to obscure their identities. Chanology is one of those attempts, and there are links between Chanology and Anonymous.
Anonymous has a multifaceted base of concerns and issues that they focus on. To say that Anonymous is synonymous with Chanology is off base since their association with Scientology is one of drawing attention to internet censorship concerns, not an affiliation or endorsement. Internet censorship being just one of Anonymous’s concerns, makes it illogical to consider them synonymous with Project Chanology. A more suiting description of their relationship might be to say that Anonymous has targeted the Church of Scientology in Project Chanology over concerns of internet censorship. If Anonymous is to be considered synonymous with anything in this regard, it should be internet neutrality.
Project Chanology and the hacker group Anonymous should not be considered the same group until there is significant and clear evidence that links the two groups together beyond a reasonable doubt. We should never assume guilt just based upon a theory until there is actual evidence that confirms or disproves the idea.
though project chanology has many similarities to the group anonymous, they should not be considered as synonymous with anonymous. People seem to have a misunderstanding of what anonymous is. It's a loose collection that is organized because of the internet. Project Chanology was very organized and had a single mastermind.
Anonymous, the international hacking group famed for hacking Sony in wake of their 'mistreatment' of a young hacker, is typically an advocate for information. Those people that intentionally hide information to avoid being exposed as corrupt or immoral according to Anonymous. Project Chanology is an offspin of that, and not a very popular one. It is only concerned with one organization and its downfall: Scientology. Anonymous used to take on meaningful things that had real impact. If Chanology is the current level of Anonymous, they truly have been defeated.