The octave buttons are used to shift the keyboard up or down in one octave increments. This extends the range of the keyboard in either direction, which lets you play notes that lie outside the number of keys available.
The more buttons the device has, the more complex the input can be.
Faders can be either channel volume faders, pitch sliders, crossfaders or even EQs.
More knobs (rotating controls) can give the user more dedicated control over the device – e.g., volume, effects, EQs, etc. Types of knobs may differ between endless type or step type.
A type of knob that has a push button functionality built in. Encoders are for browsing and selecting your digital sound files or turning on a function that makes use of a control's rotation such as sound effects or tempo/tap tempo selection.