They are concepts from commentaries/abhidhamma.
Conventional truth is whatever concept is concerned with the self.
Ultimate truth, depending on different traditions, can mean quite different things.
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Abhidhamma puts ultimate truths as the ultimate breaking down of the physical and mental elements and nibbana. Like the atoms. The goal is to be able to describe things without referring to a self. So speaking in ultimate truth can be very troublesome, as you saw my attempt above. Ultimate truth wise at this level can refer to dependent origination as the mechanism for rebirth without soul/self. And dependent cessation as the ending of rebirth for the arahants (or rather the 5 aggregates without clinging). And kamma as the volitional formations making kamma, the other aggregates receiving the results.
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Mahayana clarifies more that only emptiness is ultimate, even the elements analysed in abhidhamma are ultimately impermanent, suffering, not self. Thus without referent to self, one can use the heart sutra language. Sometimes translated to: in emptiness there is no death, no end of death etc. But TNH translation is more clear to conventional speech, death and end of death has no separate self existence.
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Personal experience of stream winners onwards, they personally see ultimate truths, so that’s why zen masters sometimes speak very illogical stuffs. Cannot easily make sense of them. They speak things like: there’s no difference between you and me, there’s no centre. There’s no self, everything is self.