It used to be that the primary test was the copper sulfide solution, and if that wasn’t good enough for some reason, they’d centrifuge it. Now, though, they have some sort of device that looks like a cross between a microscope slide and a pipette, that draws the blood up in between two thin plastic plates, and stick it in some machine. I imagine it’s some sort of optical measurement, but I don’t know the details. The machine outputs a number, so I think they don’t need the centrifuge any more.
The centrifugation was to give the PCV (packed cell number), and the machine you mention, Chronos, gives the hemoglobin.
A trick used by people with diabetes or others that have to do blood tests every day – do the finger stick on the side of a finger, rather than on the fingertip. The side is much less sensitive. Also, while the side might rub against the next finger, that’s less bothersome than the fingertip, which is constantly touching things. (And the test is still accurate; it’s all the same blood.)
FWIW, I tried to give blood today and failed the first hemoglobin stick (done by Person A), so when the Person B came in to do the second stick, I remembered this thread and asked her why a different person has to do the recheck. She said it’s so a donor can’t accuse Person A of lying about the results of the second stick in order to cause a deferral because Person A is lazy and doesn’t want another donor to deal with, or Person A doesn’t like blacks/whites/one-eyed Venusians/whatever.
I recently tried to donate blood. The first fingerstick (left hand) came up as a 12.4 (0.1 below the required threshold) so she tested again (right hand), and came up with an 11.2. How is a test that can vary by 10% from moment to moment useful? FWIW, the same person did both fingersticks.