It can be both.
More common now (since 2009-ish) is a finger prick. Even then I had venous blood draws. My doctor's office figured out he could charge me for a nurse's visit if he had her utter a few words. Since I was, then, being tested multiple times a week (i.e. multiple office visits) - and my insurance covered blood draws at 100%, I had to go to a lab which only used venous draws.
But venous draw are generally done in the arm, not the hand - unless the arm veins can't be used.
I was off and on warfarin and heparin from the 80s through 2010.
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