The main difference in Hinduism and Buddhism is that, Hinduism says that there is a permanent ultimate consciousness, while Buddhism says that the world is fleeting. Advaita Vedanta Darshana too does agree with the idea that the world is fleeting, but that's one's identity is not in the world, but in the ultimate consciousness.
Another difference that arises from this is that, Buddhism considers the mind as fleeting. But even then, we are able to remember things, because through repetition, we retain ideas. And we are able to utilize these ideas to form new ideas later on. Buddhism does realize this, but considers this an unintentional happening.
Ultimate consciousness is a substance that can reflect its own radiance, because it all there is to reflect off of. But just as a circular mirror is not its own reflection,
[This analogy is mine, but it has been shown in Trika Shaivism, and some schools of Vedanta too. The idea of the world being the radiance of Brahman is common, especially in Vishishta Advaita, but also even in most dualistic religions. The idea of reflection is a less common idea in Advaita.]
For another analogy, when a blind man touches himself, he feels himself. But this feeling is not him. This feeling allows him to recognize himself, yet it is not him. And this feeling is the world.
[This is an original idea from me, but the idea is similar to the idea of reflection.]
[Now, I do not care about original ideas in the sense of them being patents. I only care about them in ensuring that they are not blind ideas that are repeated from texts.]
But one asks, why can't the ultimate consciousness change the way in which it is touching itself? Because the ultimate consciousness is not freely touching itself, its nature is to touch itself. That's where the reflection analogy is better. Unlike humans with a mind and intentions, the ultimate consciousness does not have a mind. Rather, it is the glow of the ultimate consciousness as it is reflected on itself that is the world. The ultimate consciousness is unchanging, but the glow isn't.
[But then, doesn't this disagree with Thrika Shaivism, that considers Maaya to be freely coming from Shiva?]
No, it doesn't. It only disagrees with the idea of Neo-Advaita and others who say that Maaya has nothing to do with Brahman, and it simply ignorance that causes it. No. The world is an reflection of the nature of Brahman. This is also what Trika Shaivism considers. Shiva is not actively imagining the world. Shiva is the ultimate that is the source for all the glow that is emanating from him. It is within this glow that time and events happen. The only ignorance is in misidentification with the glow, rather than the source of the glow.