The earliest written reference to the Screwdriver is from the October 24, 1949

"In the dimly lighted bar of the sleek Park Hotel, Turkish intelligence agents mingle with American engineers and Balkan refugees, drinking the latest Yankee concoction of vodka and orange juice, called a 'screwdriver.'"

The drink got its name because the American engineers surreptitiously added vodka to small cans of orange juice and stirred the mixture with their screwdrivers

Types:

The 'poor man's screwdriver' is one part vodka, and two parts orange drink mix, such as Gatorade.
Replacing the flat orange juice with a carbonated orange drink such as Orangina produces a cocktail known  as a Hi-Fi.
A Screwdriver in which Tang is substituted for the orange juice is known as a "fuzzy cosmonaut" or a "Tang banger".
To make the beverage more palatable a sweet liquor is often added such as Amaretto. This is often referred to as a   Samerreto