What different blood tests usually require blood drawn from an artery for accurate diagnosis?

You have misunderstood something. There are no blood tests that require arterial blood; venous is always OK. (Except for occasional severely ill hospitalized patients, in whom arterial blood is sampled to measure blood oxygenation. But no blood counts, infection diagnosis, or chemistry tests require arterial blood.

The usual test on arterial blood is an arterial blood gas which provides better information on oxygenation than the test done on venous blood.