Function decoders offer ONLY auxilliary/function outputs, and DO NOT have output for controlling motor or sound.
They have a wide variety of applications, but most commonly used to add lighting, smoke, or auto-coupling control to a vehicle that has no motor. For example, many modern steam locos have a DCC decoder socket in the tender, which gives control of the motor, so a separate function decoder can be added in the boiler of that loco to provide control of loco lamps, firebox glow and other special features.
Another common use is to provide DCC control of coach lighting, which is particularly effective where the decoder supports a stay-alive capacitor which helps eliminate flicker.
Accessory decoders are static decoders on your layout, deployed to control points and lighting features. Some allow control of solenoid-style point motors, and others give fine servo-control for slow-action points. You need a DCC controller that understands how to drive accessory decoders (most controllers other than the very basic ones can do this).
Plugs / Connectors
Above are shown the connector types that come as standard on those decoders, but if you need a different connector adding then this can usually be done for an extra £4!