I don't know if there are cash-based welfare programs in India. The only thing I distinctly remember is federal government-subsidized produce, so you'd go to their shops, show your government card and pick up essential grains like rice and wheat at a significant discount. I don't think this was restricted to the very poor either; my parents were middle class and they always got our food through the government subsidy.
In TN the state government operates public kitchens intended to prevent hunger. They price a square meal of cooked food at around 4 cents each, so that even the homeless have access to decent food daily.
I can't think of any "cash for cash's sake" program at all.
There is the subsidized grains program you mention, that one is huge. Like you say it's so broad that it covers the poor, working class, and part of the middle class.
There is a subsidized cooking oil/propane program too. Again, it's pretty broad.
There is a midday meals program. Free lunch for all kids in government schools (only poor kids go to government schools for the most part).
There is a rural work guarantee. If you live in a rural area and you can't find a job, the government is supposed to provide you with 100 days of work in the year, like cleaning streets and working on government construction projects or something. That one is pretty new and I'm not sure how widespread it is.
There are a lot of loans/subsidies for various things like slum people who want to get property and stuff like that. I'm not sure how all those work.
There is a limited medical program, like you get a card where you can get up to about $1000 of medical care in a year before you have to start paying. I don't think that one is very widespread. Public hospitals are generally pretty cheap for the basics, but a bad issue can drive a poor family into debt quickly.
There are lots of quotas for dalits, lower castes, minority religions, etc. for both university spots and government jobs.
So yeah, lots of social programs. But I can't think of any direct cash welfare stuff.