Definitions

One minute of exploration on the internet easily informs all that there are 9 regional 'film industries' in India:

The Bhojpuri (Purvanchal) film industry
The Bengali (Bangla) film industry
The Hindi film industry, also known as Bollywood
The Kannada film industry
The Kashmiri film industry
The Malayalam film industry
The Marathi film industry
The Tamil film industry (Kollywood)
The Telugu film industry
(http://en.wikipedia.org/wiki/Cinema_of_India)

So it is important to be specific. My blog, for example, is principally about the largest of the regional industries, Hindi films. I have very limited experience with the other regional industries.
Also, I am against the word 'Bollywood'. I like the Hindi film industry too much to see it as the little brother of 'Hollywood'. While many Hindi films may be inspired by Hollywood films or Hollywood storylines, they are very much a genre in themselves and the industry doesn't really need to look up to its competition with a nickname invoking the others identity.

Asides from these regional film industries there is a robust independent film industry. Films by Mira Nair and Deepa Mehta, such as Water which was nominated for a foreign film Oscar in 2007 fall into this 'independent' category. The reason for this is simple. Such films are in English rather than a regional language and often the storyline is considered to be more realistic. In other words, they are closer to analytic Western films, with heavier stories, trying to teach something coherent about social, political or cultural life in India or about Indians to the foreign English speaking world.

I am inclined to also add a small but growing local language based independent film sector. Like independent sectors in other countries, these films tend to show case acting talents of unknown or rising stars or contain more thought provoking or unusual storylines/imagery.
These films are frequently produced by individuals who repeatedly work together.

As stated, I am inclined to nominate a local language independent film industry. I am sure that many Indians would not agree or would have a more appropriate name for the types of films I have in mind.

Independent film producers, by the simple fact that their films are in English, target their films to international viewership. However, regional film industries typically target Indians. Of course, criteria and conditions have been changing, especially with the ever growing Non-resident Indian (NRI) population living in UK, USA or any other country. Migration has resulted in ever greater international exposure of regional Indian films, particularly the big budget, multi-star Hindi films and growing international popularity.