I think this was mainly a confusion of terminology.
Symbol: Stylized functional drawing of a part, designed for straightforward design of a circuit. May not look anything like the actual part, pins may be arranged out of order to group similar functions, etc. Can only be used in a schematic.
Package: Accurate drawing of a PCB pattern for a physical part. May not look exactly like the real part, but contains the pads and other elements necessary to implement the part on a PCB. Can only be used in a board.
Device: contain information about a functional element. Always contains a symbol, usually contains one or more packages. The connections between the symbol pins and the package pads are defined for each package style. When you add a device to a schematic, it uses the symbol; if you have back-annotation working correctly then the package will appear on the board.