Is there a difference between paneer butter masala, matar paneer, malai kofta gravy?

Paneer butter masala, malai kofta gravy and matar paneer are part of the North Indian cuisine where the base is mostly the same with some minor variations (like excluding cumin seeds).

So essentially, you have a common base gravy for sweeter dishes like these and then you have a spicier gravy for other dishes. Many Indian cuisines have this pattern. For example, Gujarati cuisine will have red chili powder, turmeric, garlic-ginger, mustard seeds, cumin powder, fenugreek, cilantro and jaggery, etc. as a general base with some additions and subtractions of the vegetable ingredients. Similarly, you'll be able to find common base gravies across Indian recipes and cuisines.

But, when you say: "In addition - It seems to me that the same thing could be said about aloo gobi, chana masala, baingan bharta, and many other dishes - Basically the same frying of onions, ginger garlic paste and tomatoes, but with a different ingredient added at the end (for example eggplant for baingan bharta)."

You are making a generalization which is not necessarily true. These recipes can vary quite a bit based on regional tastes, specially baingan ka bharta. This dish is a signature dish and needs a seasoned hand to deliver it right.

So, you are right when you say there is a common pattern across recipes. But certain dishes like aloo gobi will exist in different forms across the country. But rest assured malai kofta, paneer butter masala and matar paneer are only prepared in the North Indian style.

Both three have some differences,they are not same in taste, texture and appearance. Paneer butter masala is a rich, creamy,cashew based gravy where red chilli powder and tomato gravy are used to prepare. Paneer butter masala taste less sweet, little spicy and having a thick smooth gravy. It is light red in colour.

And mutter paneer is a no sweet, spicy in taste dish,which is not thick smooth gravy in texture. It is light brown in colour. Additional use of green peas in mutter paneer.

Whereas Malai kofta is completely a sweet and salty dish in taste and is white colour in appearance. There is no use of red chilli,tomatoes.

You can check the recipe below for paneer butter masala to get an idea for it's taste, texture and appearance. Paneer butter masala recipe

Yes those three are very different. Paneer butter masala is paneer in tomato sauce, kofta is fried paneer balls and nabratan korma is made with vegetables.

These are all post-colonization dishes and are in their nature fusion dishes, therefore aren't authentically a part of historic Indian cuisine. This is also why a butter paneer at one restaurant tastes drastically different than the other.

The post-colonization mire-poix-style equivalent core content for North Indian dishes is up to this part of what you're describing (frying cumin seeds, onions, ginger garlic paste, tomato) and then to this is added any spices (could be more spices than what you'd listed), cream/milk/cashew, etc and any vegetables.

In an Indian restaurant in US they might use the same gravy, but back home it is different gravies.