Ahh yep, I misread that it was an IAM condition. So there are two different concepts here:
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A CloudFormation Condition allows you to optionally create a resource within CloudFormation if certain conditions are met;
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An IAM Condition limits the granted access to resources which meet the given conditions.
The Fn::Equals is for the former, while ArnLike is for the latter. Docs on IAM Conditions are here.