Direct fecal smears are less accurate and less likely to show eggs if they have a low level infestation because, unles there is fecal matter right there in the mouth of the rectal sphincter, all you are getting is residue which has been smeared across the wall of the rectum.  However, if you do a direct smear and you find eggs- you know you've got yourself a problem.  Each species of worms lays a different number of eggs or oocytes.  For example, if you do a fecal on an adult bird and you find one or two coccidia oocysts per frame, you need not treat for coccidia because each adult produces hundreds (that's not an exact number, I'm just pulling that out of my rear) of "eggs".  On the other hand, if you find one capillaria egg on an entire slide, then you definitely have to start treatment for capillaria (whipworms).  This is because the female whipworm only lays a few eggs at a time.  But if you do a direct smear and find any of these, you should treat.
 
 
A fecal floatation comes from the cecum- a lump of poo and it will place nearly every parasite egg from that lump (and anything else with a similar specific gravity) onto the slide so if you find a handful of coccidia in an adult bird- no problem (unless the bird is already immune compromised, i.e. mareks disease).  But, again, if you find even one capillaria- you treat.  I treat if I find one of anything but coccidia and this is where we get into false negatives.
 
Parasites all live and grow in a predictable cycle.  Depending on the parasite and their host tissue/organ of choice, they are either making themselves comfy, encysted in the cells of their host or they are laying eggs (that's a really simplified lifecycle but it narrows it down to the two most important stages).
 
 
It is best to use fresh poo, most eggs break down after a certqin number of hours.