Self pollinating is same flower to same flower or any flower of a cultivar to any flower of the same cultivar. So if I had two clumps of Stella de Oro blooming and each clump had many scapes and each scape had many flowers then pollen from any of the Stella flowers put on any of the Stella flowers would be a self-pollination (whether those were flowers on the same or different scapes or from the same or different clumps, etc.).
Selfing most diploids fails but they are tricksters. When a daylily is selfed it will set a pod (at the normal rate for the fertility of the pod parent and of the pollen parent). So if 'Barbara Mitchell' x 'Lullaby Baby' sets pods 60% of the time and 'Lullaby Baby' x 'Barbara Mitchell' sets pods 70% of the time then we would guess that 'Barbara Mitchell' selfed would set a pod 60% of the time and 'Lullaby Baby' selfed would set a pod 70% of the time (there are mathematical ways to estimate a predicted fertility for pod and pollen parents but I am not using those here).
The petals, sepals etc fall off the selfed flower and the pod starts to enlarge. Then within a few weeks the pods are aborted. Some diploids will accept their own pollen, for example, 'Stella de Oro' and the common lemon lily, Hemerocallis lilioasphodelus and produce mature pods with good seeds. Tetraploids are more forgiving and a greater proportion of tetraploids will accept their own pollen successfully, that is they are self-fertile and self-compatible. For diploids the seedlings from successful self-pollinations are less fit than those from cross-pollinations. In tetraploids the fitness of the seedlings from self-pollinations is not so poor as that in diploids.
