Your old iPod, if it was the type with a hard drive for storage, may have had enough storage capacity to hold your entire iTunes music library, thousands of songs. An iPod shuffle uses flash storage, and the 4th gen shuffle only has 2GB of storage; that's only enough for hundreds of songs. So, with your old iPod, you may have set it up to sync your entire iTunes music library. But with your new shuffle, since your entire iTunes music library is not likely to fit, you have to specify a portion of the music library to sync. Unless you do that, the shuffle still "syncs" when you connect it, but it syncs nothing.
If the iTunes sidebar (along left side of window) is not visible, from the menu bar, under View, select Show Sidebar. When the shuffle is connected, it appears in the sidebar, under DEVICES. Select the shuffle there. To the right, its Summary screen is shown. Toward the top, where it says Summary, click on Music to the right of Summary. This Music screen is where you tell iTunes how to sync songs the shuffle.
One convenient way to set this up for a shuffle is to create a new playlist in your iTunes library, and put all of the songs you want on the shuffle on that playlist. (Or you can use an existing playlist.) Back on the shuffle's Music screen in iTunes, check the checkbox for Sync Music. Choose the option to sync Selected playlists, artists, albums, and genres. Below that, find that playlist under Playlists and select (checkmark) it. You can select other items on those lists if desired.
When you click Apply, the songs in your selection(s) sync to the shuffle. Going forward, to update the shuffle's songs, just update that playlist in your iTunes library (add/remove songs). The shuffle does not need to be connected. The next time you connect the shuffle (or click Sync if already connected), iTunes automatically updates the shuffle with the same changes.
This is not any different from how your old iPod worked (for syncing). The difference is that with your old iPod, it had enough storage space to allow you to set it to sync your Entire music library on the iPod's Music screen. With your shuffle, you need to be more specific.
but under File-Devices in iTunes, sync is gray.
That menu bar item is disabled unless a device is selected in iTunes. When you select your shuffle in the sidebar, that command becomes enabled. However, most people do not use the Sync command in the menu bar, because when the iPod is selected in iTunes, there is a Sync button near the bottom right corner of the window.
