The "regular" files you were downlding would have been mp3 files. You can also downld other formats like aac (m4a), mp4, ogg, wma (eek!), & the odd lossless format.
Perhaps you've forgotten about this: Burning an audio CD from your MP3's

If you've downlded mp3 files you can't play or burn then it sounds like you're missing the appropriate codec, id3 tag or they're corrupt. See T3 Spammers; mp3 Bit-Rates Versus File Sizes