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We knows that in a critical system and self organized criticality we have long range interaction due power law decay in correlation. Is this fact equivalent to the butterfly effect?

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No, or at least not in the sense the phrase "butterfly effect" is normally used. Well, possibly, but only if the critical system is chaotic.

The phrase is normally applied to systems that show chaotic behaviour. In such systems the trajectory of the system is very sensitive to the starting point i.e. if you take two points very close together in phase space the trajectories from those points will diverge. Hence the claim that a very small change to the system, such as a butterfly flapping its wings, will cause a big change in the future evolution of the system.

Critical systems may well show chaotic behaviour, and if so then I suppose the phrase "butterfly effect" does apply to them. However if this is the case the phrase would be used because they are chaotic not because they're critical.

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