What I have read about drift is that codes (Im talking about ASCE & ACI) intention is to limit all these three states; serviceability, damage, and collapse. Codes distinguish and set criteria only for horizontal component of drift (horizontal racking) whereas in a building vertical component of drift also exists. We have Damage Index to know the extent of damage that's been done. Damage Index takes into account the effect of both horizontal and vertical components of drift like shear strain.
This is one of my favourites about drift. See the attachment.
Dan Berding Thesis.pdf