Is there a consistent interpretation of what is “Originated”?

The definition of origination for HMDA is a funded / closed loan. This definition also applies to the institutional and partial exemption thresholds.

Only originated (closed) loans count toward the loan-volume thresholds. If a threshold is met, the institution reports all applications that it receives, originates, and purchases for that type of transaction (either Closed-End Mortgage Loan or Open-End Line of Credit, or both, if both thresholds are met).