Confusion with checkboxes

I have a first gen. iPod touch with the most up to date iTunes on my MacBook Pro. I am having some trouble figuring out the check boxes. I have some songs unchecked in iTunes so they won't sync to my iPod, but when I put the songs in a playlist iTunes skip past them. Is there anyway I could have unchecked songs in my iTunes library that won't sync to my iPod, but will still play when on shuffle on my MBP? I know this is kinda confusing, sorry. Thanks in advance!