Central angle = Angle subtended by an arc of the circle from the center of the circle.
Inscribed angle = Angle subtended by an arc of the circle from any point on the circumference of the circle.

Figure below shows a central angle and inscribed angle intercepting the same arc AB. The relationship between the two is given by

if and only if both angles intercepted the same arc. In the figure below, θ and α intercepted the same arc AB.