Both are correct. Each has a different nuance. If you 'noticed' your wallet was missing, one of your physical senses (sight, touch, etc) has made you aware your wallet is missing. If you 'realized' your wallet is missing, it is more a cognitive event, rather than a physical sense why you are aware your wallet is missing. You have mentally drawn a conclusion your wallet is missing - maybe your physical senses led to this, maybe something else.

To come to a realization means that you understand the significance. To notice something means you see it, and perhaps you appreciate it. To stress the difference between these words, I would say that I NOTICED the blind man crossing the street. However, I would say that I REALIZED he was in danger when I saw the car racing toward him. I might notice a wallet on the table, but I then would realize my husband had forgotten it there and was driving to work without it.

You noticed that your pocket was empty (a fact at a certain time). You were concerned that your wallet might have been lost or stolen. (“lost” could be used to cover both cases) You looked around and didn’t find it anywhere else. You realized it was lost. You concluded it was lost. Your sentence with realize would be slightly better as After I got home, I realized that I’d lost my wallet.

* Noticed is slightly better for things you see. * 'true' isn't the right word to use there. Use 'correct' instead. I write on italki <- is true. I don't write on italki <- is not true. I right on italki <- is incorrect.

You noticed that your wallet was missing, and then realized that you had lost it.