Unsurprisingly, when you have a continent-sized country with many different languages and cultures, a very long and rich history in all kind of arts and probably the most prolific national cinematography in the world, the end result is that "indian films" is a term that covers a very complicated universe.
In the past few years, some recent indian productions have been screened in my city (I think it's a mix between some indian cultural association and indian studios using world wide sales as a promotional argument at home). Between those, some oddities I stumbled upon here and there in festivals and some more "arty movies" that ended in theaters, I maaaybe have seen 30ish indian films in my life. So at this point, the main thing I understand is that I don't understand much!
Like, for instance you mention masala films (a term I learned today thanks to you!) that is, to paraphrase wikipedia, films that mix action, comedy, drama, singing and dancing, with an emphasis on colorful high level production and costumes. It's supposedly a style that emerged in the '70s and that is still very popular today in all the movie productions hubs in India. But I feel that even before that, India had its how take on musical films. One of the few classic indian film I saw is
Pyaasa (1957) (probably not that easy to find, but clearly a masterpiece - EDIT: actually it's very easy to see,
it's on youTube in full!) and it already has the very long duration (2h33) and many song sequences that clearly are not sung by the actors (something that is also peculiar: the lyricist and the actual singers are also stars when it comes to the promotion of the films - our musical films tend to only focus on the composer), but there is no dancing to be found. So not really a masala, but not really your average Hollywoodian musical film either. Complicated...
Wikipedia mentioned a good example of a non-indian masal-inspired film: Baz Luhrmann's Moulin Rouge!