An engineer, Phillips was an acquaintance of John P. Thompson,[4] who sold his self-centering design to Phillips in 1935 after failing to interest manufacturers. Phillips formed the Phillips Screw Company in 1934, and after refining the design himself (U.S. Patent #2,046,343, U.S. Patents #2,046,837 to 2,046,840) for the American Screw Company of Providence, Rhode Island, succeeded in getting the design quickly adopted by industry.[5] One of the first customers, in 1936, was General Motors for its Cadillac assembly-lines.
Straight slot screws, Phillips heads weren't invented and in common use. Phillips screws were invented in the mid 1930's, and I never saw one until sometime in the late 40's early 50's, and frankly I didn't like them at the time.
These are a couple of machine screws showing the different heads. The first is straight slot, the second Phillips head.