As Vero_F1 has pointed out, you are looking under the wrong heading. To add to what Vero has told you, use the screenshots below as your guide:
To look on the iPod from iTunes:

that will display the Device/Settings/Summary pane (as shown in your first screenshot.
Now switch to the heading immediately below the Summary pane; the Device/Settings/Music pane (1.):

This pane (shown above) is where you determine what is added to, or removed from, your iPod. It also assumes that you have your iPod connected to the same iTunes as you did when you added the music to it originally. Note that the same iTunes means:
- it is the same computer
- iTunes has not been uninstalled and then re-installed
- the computer has not had major repairs (i.e. replacement motherboard)
- If the information above is not how your iTunes is set, post back with details of what is different
- If the criteria above is okay, you should find that Sync Music (2.) is ticked (checked). It's step 3 that is now important.
- if you have Sync Entire music library ticked, then all of your music will have been added to your iPod
- if you have sync selected playlists, artists, albums and genres ticked, then the various section 4 panels will allow you to deselect music that goes onto your iPod
Some of this may appear confusing. Feel free to post again, asking for explanations or further information about anything I have written here, that might help you achieve your goal.