If you use the delegation tab of a GPO and click advanced you can assign the Read and Apply permissions to a user or group. if you do this (and if the GPO is linked to the correct level) then the GPO will apply to that user or group. more than this if you do use the delegation tab and click advanced and assign the read and apply permissions to a user or group then that user or group will appear in the security filtering section of the GPO.
in reverse if you edit the security filtering section and add a user or group then that user or group will appear on the delegation tab and if you look at advanced you will see that the user or group has appeared there with the read and apply permissions.
So the security filtering and the delegation tab advanced are doing the same thing!
However using delegation tab you can assign additional permission for the GPO so you could assign permission to edit the gpo for example. in short the delegation tab is more powerful but if you just want the GPO to apply to a user or group you can use either the security filtering or the adv section of the delegation tab.