Some apps (e.g. Angry Birds) I'm finding only on iTunes, isn't there a way to buy in directly on my iPhone/iPod touch?
It is very likely that the iTunes store in your country (Brazil after your profile) does not have all the apps from the US AppStore. Developers can choose if they want to make their app available in all or just some countries. Since the website of Apple shows the content of the US AppStore by default it might have led you to believe that you can buy the app with your account.
If @Andris got your problem right then, if you live in Brazil, you have the same problem I have. :-)
I mitigate it having a second account in the US Store. That allows me to download free stuff that is only available there (games and music apps like Shazam), and when I wish to buy an app I buy an iTunes Gift Card in eBay.
Another solution is moving your account to the argentinian store, which has a more "relaxed" policy and allows apps that doesn't appear in the brazilian store. I've never tried that, but I was told that you can create an account there with a credit card that has a billing address in Brazil. That is not accepted in the US and UK stores, for example.
Have you checked that you are logged in with the same account in both stores? Itunes sometimes doesn't have all apps available in all regions and you can have more than one account in the same library. If you are not logged in with the same account, I'd suggest you do login with the same account in both devices.