The 4th gen shuffle can use playlists. Are you playing songs on the shuffle from a playlist, or from the All Songs list?
If you sync a playlist that is in a particular order (in iTunes), but you play the songs from the All Songs list (on ths shuffle), they will not play in the playlist's order.
You use the VoiceOver button on the shuffle to switch playlists (press and hold the button). This article has more info on using VoiceOver on the shuffle.