Conventional truth, as I understand it, would be truth according to ordinary worldly conventions and language, i.e., a table has legs and a surface, or, a being form body subject to rebirth. Also included would be proofs deriving from observation, evidence and inference according to something like a court. Ultimate truth is the truth according one who has mastered the path, i.e., that describes the nature of dependent origination of a chair, or the khandas of a being, etc. Such that, the metta and karuna are emotions aspirants of the path share with non-aspirants. Whereas, the practice that involves discerning phenomena in their ultimate truth is unique to the path.