Several discourse annotated corpora now exist for NLP exploitation. Nevertheless, it is not clear how these annotations compare: are they incompatible, incomparable, or do they share some inter- pretations? In this paper, we relate three types of discourse annotation as found in: (i) the RST Tree Bank corpus, (ii) SDRT corpora DISCOR and ANNODIS, and (iii) dependency tree structures. The latter have not yet been used in actual annotations, but represent elementary substructures which are interesting for automated parsing. Specifically, we discuss two ways of interpreting RST trees by taking discourse relations as semantics operators, one is fully specified, the other one underspecified. We also provide an underspecified semantic interpretation of dependency trees. We define trans- lations between RST and DT that preserve these underspecified interpretations. On this basis, we design similarity measures that quantify the loss of information implied by these translations. Over- all, these translations and metrics provide a unified framework that will hopefully enable us to take advantage of the various existing discourse annotation data that are available for automated tasks.