In Northern Lights, children (and the adult nurses) undergo intercision at Bolvangar. Many of the children die, but some like Tony Makarios survive (if only for a time) and adults definitely survive. It appears that the bond between human and daemon, in the case of the adults, is broken. So why are the effects much less serious than in the case of a spectre attack? When adults are attacked by spectres, they lose all function and can merely gaze dumbly. So what is the difference between the intercision, where one merely loses one's 'spark', and a spectre attack, where one loses interest even in one's own survival?
If you read the article on Intercision on the His Dark Materials wiki, they discuss early forms of Intercision, as performed by the Tartars and African tribes, which resulted in the creation of Zombis, workers who could no longer think for themselves. This sounds very similar to the effect of the spectres eating the daemon.
As to what the difference is, I suspect it is a matter of trauma. The African method is described as a forced separation by steadily increasing the distance between the human and their daemon. Compare this to the Maystadt or Silver Guillotine methods, which cut the bond directly, more surgically, creating less trauma. Much like how it is easier to survive having a limb surgically severed than it is to have the same limb chewed and ripped off, it is easier to survive having one's soul surgically removed than having it ripped away by creatures gnawing away at it.