There are multiple ways to decompose lift and drag forces, and they are unfortunately not compatible with each other.
If you know the flow field (for example because you ran a CFD simulation), then to compute lift and drag, you need to integrate:
- pressure forces (i.e. local pressure times surface normal, over area)
- viscous forces (local viscous stress times shear direction, over area) shear stress is tangential to the local surface, but because not all surfaces are tangential to the flight direction, this influences both lift and drag (though usually a lot more to drag).
That gives you two force vectors, and after you added them up, you can then decompose them into one component which is parallel to the inflow direction (drag), and one which is normal to it (lift). (let's forget spanwise forces for now...).
Looking at drag, you can then of course see which part comes from the pressure forces and which comes from the viscous forces.
Next, induced drag: This is actually a somewhat theoretical definition, and most people today speak about "lift-dependent" drag. This means: How much more drag is the airfoil producing because it produces lift? Assuming an uncambered airfoil, the lowest drag is at AoA=0°, when lift is also zero, so all additional drag we're getting at AoA=15° is lift-dependent.
Assuming a cambered airfoil, the lowest drag is actually not at zero lift, and also not at AoA=0°, so at lowest drag, it's actually producing some lift -- so ... negative lift-dependent drag! Just look at these drag polars:
Does that mean we have negative induced drag? Our definition is already becoming difficult to use. So let's keep the airfoil uncambered for now, meaning that the lowest drag is also at AoA=0, where we produce no lift.
So, under these circumstances, what happens to drag when we increase AoA? Of course, pressure on the upper side of the wing reduces, and it increases on the lower side. This means we're getting a pressure force which is pointing mostly upwards (lift) but also somewhat backwards (drag). But we're accelerating the flow on the upper side, which increases friction there. We're decelerating on the lower side, but that effect is a bit smaller. This means we're getting some additional friction drag. But that's not all! Because of the additional friction on the upper side, the boundary layer grows faster than it would otherwise, changing the streamlines, which in turn changes the pressure distribution, and causes additional pressure drag. This means: If we switched friction off now, we'd actually reduce pressure drag, too!
So, really, we can't point at the change in pressure drag and call it induced drag.
Now, if we make some more simplifying assumptions -- the kind that people used to make all the time when they were still using pencil and paper to design airplanes -- that's when things finally start to add up.
This means we're assuming simple potential flow, and maybe we're adding some estimate of viscous drag based on flight speed and surface area, which is not affected by pressure distribution. In that case, we would have no pressure drag on our symmetric airfoil at AoA=0°, and all the pressure drag we're getting at AoA=15° is purely because the pressure on the airoil is pushing normal to the surface, the upper side is also facing backwards to some extent, because it's at incidence to the flow. Now, all the pressure drag is indeed due to lift, and viscous drag is not affected by lift.
So, until now I was talking about "lift-dependent" drag. But what about "induced" drag? Even the Wikipedia article on induced drag doesn't make a difference between lift-dependent and induced drag, so how big can it be? Fairly large, actually. The most common definition for induced drag is the drag generated because the wing produces trailing vortices. So all the kinetic energy in the wing-tip vortices (but also in the vortex sheet behind the wing wherever the lift is changing in spanwise direction) needs to come from somewhere, and that's called induced drag. At least in simplified physics, that is indeed completely pressure drag -- but it does not necessarily explain all pressure drag. Imagine for example an infinite wing. No change in lift distribution, no trailing vortices, but it must have some pressure drag! Mathematically, this can be solved by assuming that when the wing accelerated or increased AoA, it generated a parallel vortex which it left behind, and keeps feeding via two imaginary wing-tip vortices at infinity. But if you measure a 2D profile in a wind tunnel or simulate one with modern CFD methods, the lift-dependent part of drag is much larger than that, because the theoretical induced drag is pretty small next to all the real effects which happen on top of it.
Now, if you take one more step towards reality, and include cambered airfoils, viscosity, boundary layer displacement, and if you're going fast enough also compression shocks (which produce "wave drag", which another factor influencing viscous and pressure drag...) -- that's when "induced drag" becomes fairly theoretical.
So why on earth does anyone still use it? Precisely because it is simple to compute in simple physics models, where you ignore a lot of real effects. That's when it still does tell you what the lowest achievable lift-dependent drag for your wing shape would be, if all those nasty interactions between pressure field and boundary layer, separations, shock waves and other complications did not exist. This means: Induced drag is a useful construct to explain why lift always produces drag, why long slender wings can be more efficient at producing lift, and how much more efficient. But in a real flow, there's not really a way to extract it separately.
Footnote: Of course there are methods to at least approximately extract the different drag components. The best-known tool to do this is Onera's FFD tool (which only few people outside Onera get to use...). I did not find the original paper quickly, but here is the extension to unsteady flow. You can see the math becomes pretty complicated very quickly. You can also see that they provide a lot of drag components, but a closer look shows that although they include induced drag, and a lot of other components, they're not all adding up to total drag -- that's because there are lots of ways to decompose drag, and most of them don't neatly align.