Honestly, Nagel's rhetoric is not terribly clear on the distinction of the two terms.
I get the sense that by "impression" he means something vague, not certain, unverified, general; like an impressionist painting is to a photograph; and I think he means something like a memory as well as a "sense impression" (p8) of the case. His comment about "the impression of royalties" also makes me think there is inference at work with his use of "impression". On page 12 he uses "impressions and experiences" as if there are experiences and our impressions of those experiences(impressions of impressions?).
By "perception" he seems to mean what is perceived by the senses and also how it is interpreted. Note that on page 10 he seems to distinguish perception from memory. So perception seems to be more about the immediate experience of the now, and maybe impressions are of the now, but also last into memory?
So... if we [1.] subtract the external world there can be no [2.] "immediate sense impressions turning into memory impressions" and only [3.] mental interpretations constituting reality.
In "What Does It All Mean" Nagel uses "impression" only ten times and "perception" six:
Nagel's uses of "Impression"
Whatever you believe — whether it's about the sun, moon, and stars, the house and neighborhood in which you live, history, science, other people, even the existence of your own body - is based on your experiences and thoughts, feelings and sense impressions. That's all you have to go on directly, whether you see the book in your hands, or feel the floor under your feet, or remember that George Washington was the first president of the United States, or that water is H2O. Everything else is farther away from you than your inner experiences and thoughts, and reaches you only through them.
If you try to argue that there must be an external physical world, because you wouldn't see buildings, people, or stars unless there were things out there that reflected or shed light into your eyes and caused your visual experiences, the reply is obvious: How do you know that? It's
just another claim about the external world and your relation to it, and it has to be based on the evidence of your senses. But you can rely on that specific evidence about how visual experiences are caused only if you can already rely in general on the contents of your mind to tell you about the external world. And that is exactly what has been called into question. If you try to prove the reliability of your impressions by appealing to your impressions, you're arguing in a circle and won't get anywhere.
The most radical conclusion to draw from this would be that your mind is the only thing that exists. This view is called solipsism. It is a very lonely view, and not too many people have held it. As you can tell from that remark, I don't hold it myself. If I were a solipsist I probably wouldn't be writing this book, since I wouldn't believe there was anybody else to read it. On the other hand, perhaps I would write it to make my inner life more interesting, by including the impression of the appearance of the book in print, of other people reading it and telling me their reactions, and so forth. I might even get the impression of royalties, if I'm lucky.
On the other hand, to conclude that you are the only thing that exists is more than the evidence warrants. You can't know on the basis of what's in your mind that there's no world outside it. Perhaps the right conclusion is the more modest one that you don't know anything beyond your impressions and experiences. There may or may not be an external world, and if there is it may or may not be completely different from how it seems to you — there's no way for you to tell. This view is called skepticism about the external world.
An even stronger form of skepticism is possible. Similar arguments seem to show that you don't know anything even about your own past existence and experiences, since all you have to go on are the present contents of your mind, including memory impressions. If you can't be sure that the world outside your mind exists now, how can you be sure that you yourself existed befare now?
...But without some possibility of a correct view of how things are (either yours or someone else's), the thought that your impressions of the world are not true is meaningless.
If this is right, then the skeptic is kidding himself if he thinks he can imagine that the only thing that exists is his own mind. He is kidding himself, because it couldn't be true that the physical world doesn't really exist, unless somebody could observe that it doesn't exist. And what the skeptic is trying to imagine is precisely that there is no one to observe that or anything else — except of course the skeptic himself, and all he can observe is the inside of his own mind. So solipsism is meaningless. It tries to subtract the external world from the totality of my impressions; but it fails, because if the external world is subtracted, they stop being mere impressions, and become instead perceptions of reality.
Nagel's uses of "Perception"
But what else is there to depend on? All your evidence about anything has to come through your mind — whether in the form of perception, the testimony of books and other people, or memory — and it is entirely consistent with everything you're aware of that nothing at all exists except the inside of your mind.
The skeptic's answer is that the process of scientific reasoning raises the same skeptical problem we have been considering all along: Science is just as vulnerable as perception. How can we know that the world outside our minds corresponds to our ideas of what would be a good theoretical explanation of our observations? If we can't establish the reliability of our sense experiences in relation to the external world, there's no reason to think we can rely on our scientific theories either.
So solipsism is meaningless. It tries to subtract the external world from the totality of my impressions; but it fails, because if the external world is subtracted, they stop being mere impressions, and become instead perceptions of reality.
If a thing is incapable of movement, it can't give any behavioral evidence of feeling or perception.
But there is also a philosophical question about the relation between mind and brain, and it is this: Is your mind something different from your brain, though connected to it, or is it your brain? Are your thoughts, feelings, perceptions, sensations, and wishes things that happen in addition to all the physical processes in your brain, or are they themselves some of those physical processes?
The question of survival after death is related to the mind-body problem, which we discussed earlier. If dualism is true, and each person consists of a soul and a body connected together, we can understand how Ufe after death might be possible. The soul would have to be able to exist on its own and have a mental life without the help of the body: then it might leave the body when the body dies, instead of being destroyed. It wouldn't be able to have the kind of mental life of action and sensory perception that depends on being attached to the body (unless it got attached to a new body), but it might have a different sort of inner life, perhaps depending on different causes and influences — direct communication with other souls, for instance.
For a clear use of "perception" and (only one use of "impression"), you might dig this article, "Perceptual Intentionality."