Nice description here https://supportforums.cisco.com/discussion/11700441/what-difference-between-default-vlan-and-native-vlan.
SAY you have a trunk between switches and you don't declare a native vlan (and you don't intentionally use VLAN 1). Then VLAN 1 traffic will pass from switch to switch with no tag, and all other vlans ARE tagged.
Say you intend to have vlan 10,20,30 passed between switches and you set native vlan 10 on the trunk AT BOTH ENDS. Then vlan 10 isn't tagged, and 20, 30 will be. If you'd set the VLANS ALLOWED, then vlan 1 would be blocked if not included.
Remember tagging is normally ONLY between switches; gets added to the packet before leaving one switch (if not native) and gets stripped and redirected appropriately on the "other end" of the link.
If inconsistent tagging is used (i.e. vlan 10 native on one side, and vlan 20 native on the other), I think it's platform dependent... Some switches won't bring up the trunk at all. Some older releases then might bleed traffic from one vlan that is native on one end, to the vlan that's native at the other, as there isn't a tag to identify the traffic.