A song in which text is set to verses of repeated melodic material is typically referred to as a "verse-chorus" song. This structure features verses that tell a story or convey the song's message, while the chorus, consisting of repeated melodic material, serves as a memorable and catchy section that often encapsulates the main theme or emotional core of the song. Another term for this style can be "strophic" form if the verses have the same melody but different lyrics.
If you mean a specific genre or style, pop songs often follow this structure, as do many folk songs and traditional music.