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The bed is from a 63-66. That bed Style is called a styleside, Ford of Canada called it a flushside initially. The flareside style of bed is what the general calls a stepside.
Lower pic from 1957/63 catalog: Correct Styleside bed used on the following: 1957/60 F100/350, 1961/65 F100/250 4WD; 1961/66 F350; 1962/63 F100/250 2WD; 1966 F250 4WD