Update (Sorry for the length, but this is not a simple issue):
After doing a bit more investigating, it appears this “streaming” vs. “not streaming” issue is a bit more complicated than has been stated. If you tap on a song in an album, it will download it, but not in the traditional sense. It downloads it and a few songs forward in the album. But it is downloading it to a streaming cache. This is so there is no lag in going from the playing of one song to another…as was the case in iOS 5.1.1. I don’t know how big the streaming cache will get before some automatic clean-up process is done by iOS 6 if even any clean up is done. Maybe you have to manually delete the songs from the cache.
These songs in the streaming cache do look and act like downloaded music, because they are. If you do turn on Airplane Mode, as has been stated earlier in this discussion, the songs will continue to play because they ARE on your phone in that cache. Also, if you turn off “Show all songs” you WILL see those songs that are in the Streaming Cache…just like you would if you had “really” downloaded them by tapping on the Cloud icon with the downward arrow for the album. One hint that you have not “truly” downloaded the song when you just tap on it is that the Cloud icon does NOT go away. It remains. That’s because by tapping on the song, you have streamed it AND placed it in the Streaming Cache. It has NOT been downloaded and stored in your Music storage area. At least, that is what I have been able to gather from reading and experimenting with my phone.
The big issue here, IMO, is that this Streaming Cache is taking up memory on your phone. For those of us who subscribe to iTunes Match to control how much of our phone’s memory our music takes, it remains unknown how big this cache is allowed to get before it is cleared out…again, if it is cleared out at all. Maybe it is cleared out after a certain amount of time. I have NO idea and Apple sure has not made an attempt to explain this (or if they have, the explanation is really hidden well!).
I know other streaming music services excute somewhat the same procedure, but it's more hidden. Apple lets you see this streaming cache. That is not necessarily bad, but it is confusing when this streaming cache looks like normally downloaded music in many ways.
I think there is definitely room for Apple to tidy up and ramp up this whole iTunes Match business. It has become so complicated I might as well get my PhD in quantum electrodynamics instead.
What ever happened to, “It just works.”