a control system is "stable" if, upon a perturbation (like a gust or up/downdraft), the system will naturally return to its unperturbed state with your hands off the controls.
a plane exhibits "neutral" stability if, upon a control input from the pilot or a gust perturbation, the plane will not right itself if the pilot takes his or her hands off the controls, but neither will it diverge and fly itself into a steeper turn, roll, or pitch attitude hands-off.
"negative" stability means the moment you take your hands off the controls, the plane will by itself pitch up or down, roll left or right, or skid one way or the other. it cannot be flown hands-off unless it has an artificial stability augmentation system built into its control hardware.
A control system is "controllable" if pilot input is successful in recovering from a perturbation. But without pilot inputs, a "controllable" system will not necessarily by itself recover from a perturbation.
Maneuverability refers to the airplane's overall sensitivity to control inputs from the pilot and the effectiveness of the control surfaces over their control range.
An airplane that is highly maneuverable MIGHT be unstable- that is, it MIGHT not fly hands-off because of how sensitive it is to control inputs or gusts. In general, a high degree of maneuverability usually is associated with marginal stability.