Syncing devices and music playback

[Dvabau]

I have an iMac, iPhone and and iPad and will often switch from one to the other. How do I get them all to sync up without having to download all the music to each device. By syncing, I mean that playlist content is identical and that one device can pick up where the other left off. I guess I am still a bit fuzzy on exactly what syncing does versus making your files available offline does. Anyway, after listening to a playlist on one device in the random mode, it is really annoying to have the other devices ( say switching from the iMac to the iPhone) play the very same songs again. I know there are issues with the randomization on one device ( I will hear the same songs repeatedly) but the issue is exacerbated when switching devices.

Thanks,

Dana