Is it possible for different insurance companies to have different definitions for ECI claim? I am asking in the context that both company cover that same ECI condition.?

Yes, this is possible and in fact common. As a matter of fact, the Life Insurance Association Singapore only mandates the use of their definitions for the industry list of 37 conditions at the severe stage.

Other than that, the respective insurers have the freedom to define their own conditions when a claim becomes admissible.

You may read more about it here: Life Insurance Association Singapore (LIA) Critical Illness Framework 2020

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Yes, since there is no standardization of ECI definitions, each insurer's definitions may have differences from one another.

So there is a need to look closer and find for any weird exclusions or more narrow definitions.