This article deals with two different aspects of "regular homophony" in comparative historical linguistics. "Homophony" is used here as a cover term for both polysemy and homonymy, i.e. all the cases where a word is given several meanings in a dictionary. Our results are based on the semi-automatic analysis of regular homophony in RefLex, the richest online lexical database, which gathers 1,150,000 words from 1289 sources, covering 785 African languages (as of 2018). We show that the first aspect of regular homophony, i.e. regular polysemy, may be effectively used for semantic reconstruction and for the finding of new cognates. An Appendix gives the inventory of all regular polysemic links found in the RefLex corpus for notions included in the Swadesh-100 list. The second aspect, regular homonymy, may be effectively used for the finding of regular sound correspondences between related languages. Such correspondences may even be set up between genetically distant languages, without having to rely on intermediate reconstructions.