In the songs of the 50s to 80s a very similar structure is heard. It may begin with an intro line, e.g. in the aayegaa aane walaa, one hears Khaamosh hai zamaana ... Then there is intro music. Then the sthaaee or the refrain. More intro music, the first antaraa or stanza, followed by more interludes and stanzas.
But if one listens to songs from the 30s or early 40s, in most songs, there is hardly any interlude music. The singers start singing, keep singing and singing till the end. The music is in the background playing almost a secondary part.
The sthaaee-antaraa form became standard some time during the late 40s. Many people believe that it was Anil Biswas who did that. But it is a matter of ongoing research.