Maybe you’ve noticed that there are several different colours for Indian license plates. For most of us, it’s enough to know that private vehicles have white plates with black lettering, and taxis, auto rickshaws and other vehicles for hire have plates that are black on yellow. Whenever you are looking for a taxi, whether shared or not, check for yellow plates. All commercial vehicles have yellow and black plates and require the driver to have a commercial license, except for cars you hire to drive yourself. These can be used for any commercial purpose without the driver having to have a commercial driving permit. Self-drive cars have yellow on black plates.
Cars with white plates are not allowed to be used for commercial purposes, though I’ve noticed that they often are.
Diplomatic plates (including for the UN), which indicate diplomatic immunity, are blue, while military vehicles have white on black plates. There are also red plates designated for use on test vehicles, but you aren’t likely to encounter those.
The President of India and state governors travel in official cars that have the Emblem of India in gold embossed on a red plate rather than a license plate. They always cause traffic jams wherever they go, of course.
License plates in India are supposed to be standardised, but you still see some that have hard to read scripts or numbers that are too small to see from any distance, and some are in local scripts.
The first two letters indicate the state of registration. For those who are interested, more details can be found in Wikipedia. Incidentally, plate spotting is a good game to keep the kids occupied while traveling.