The order of the symbols on the Apple II corresponds to the ASCII symbols 33 to 41, in that order. This layout was used on a number of other microcomputers (including the Commodore 64 and the BBC Micro), and dated back at least to the 1970s: in 1974 Popular Electronics ran an article on how to build your own ASCII keyboard.
Despite this, IBM chose to use a non-ASCII-based layout for their keyboard. Apple later abandoned the ASCII layout for the Macintosh in 1984, adopting a similar layout to IBM's PC.
Obviously with the growth of the PC clone market, the PC layout would become a de-facto standard, and ASCII keyboards were relegated to history. But why were there two different layouts in the first place?
Note that the "PC" layout for the symbols was not a novel invention by IBM for it's PC: it had already been seen on the Space-cadet keyboard, VT100 terminal, and the Xerox Alto. The point remains that there were two different layouts in use at the same time.