Stabilizability as a weaker notion
The logical way to put it:


A system is stabilizable when closed-loop poles can be placed in a region contained within the left-half of the s-plane.
A system is controllable when closed-loop poles can be placed in any desired position of the s-plane.
The left-half of the s-plane is a subset of the s-plane.


Therefore, when a system is controllable, it is stabilizable. You can place the closed-loop poles anywhere, including a region in the left-half of the s-plane.

When a system is stabilizable, controllability isn't implied. You can place the closed-loop poles in a region contained within the left-half of the s-plane, but not necessarily anywhere in the s-plane.