Is the shear centre of a wing the same as its aerodynamic centre?
No. These are very different things.

The shear centre (SC) is a purely mechanical (structural) feature of the wing design. It is a point along the chord such that application of force - no matter what force - causes the wing only to bend but not twist.

Unlike the aerodynamic centre (AC) and centre of pressure (CP), it makes no sense to talk about a single integral point for the whole aircraft. An SC can be found for each cross-section of the wing, and it is the chordwise relation of the SC to CP and CM (centre of mass) of the section that is important to aircraft designers.

Designers can control where the SC will be. If we could make the SC match the point of application of the integral force at this section, we wouldn't need much of the torsional rigidity, and could make the wing lighter.

Unfortunately, this is not practically possible. First and foremost, the CP, the integral point of application of the aerodynamic force in flight, moves forward and backward depending on the angle of attack (AoA). This is just the nature of aerodynamics.

Typically, for a straight wing CP will be behind SC for small angles of attack and ahead of it for large angles. This is rather unfortunate, because this means that at a high G load (esp. at moderate speeds), or in an updraft, the wing will twist to an even higher AoA. This positive twist at the max load (typically 1.5 × rated load) is often one of the critical design cases, so in practice we want SC closer to the forward-most CP location. A clever application of SC can make the wing twist negatively and dampen its own oscillations.

CM of the wing section is nearly always behind the SC. In normal flight, static aerodynamic loads prevail over weight of the wing itself, so this doesn't matter much. However, when we start analysing aeroelastic modes, CM location becomes important. To avoid flutter, a common solution is to move CM closer to SC by installing some dead mass at the leading edge. This often proves to be easier and lighter than increasing torsional stiffness. If we can, we would install some useful mass there, such as an engine.

I didn't talk about AC yet. This is because it has nothing to do here. AC is a very theoretical point introduced for convenience of stability analysis. Any force can be broken into a moment and another force, and we just split lift such that part of it acts at CM, and part at another point. Because CP normally moves linearly with AoA, we can make it such that all changes to lift due to AoA 'kind of' happen at a fixed location. But in reality, of course, lift just increases and moves forward with AoA. The structure and aerodynamics have no idea about our mental exercise.

It is perhaps this fixed location of AC that lets it be confused with SC, which is also fixed. But they have nothing to do with each other. Structural engineers don't need to know about AC at all (they just need to ensure the aircraft CM is in a certain range they are told), whereas flight dynamicists hardly ever talk about CP but always use AC as the reference point (along with CM).