Profile drag is the term for skin friction and form drag on a 2D body. We do not talk about profile drag on 3D bodies.
3D bodies still have skin friction and form drag.
In this picture, the thickness of the boundary layer is exaggerated.
Recall that the pressure drag around a 2D inviscid closed body will be zero. This is because everything cancels out just right.
Next, we treat the flow outside the boundary layer as inviscid. It produces a pressure distribution that pushes on the outside of the boundary layer.
Next, we assume that the pressure 'across' the boundary layer is constant (this goes with it being thin). So, we apply the pressure distribution from the inviscid flow on the outside of the boundary layer to the airfoil shape. We can integrate this pressure to get the lift.
If you really understand each of the above steps, you're ready to understand form drag. If you aren't, then re-read these steps again and think about them.
What happens to the boundary layer at the end of the airfoil?
It keeps going.
The inviscid body (around which the pressures sum to zero drag) would need to continue on the outside of the boundary layer to infinity.
But we can't deal with a pressure distribution that goes to infinity. So instead, we cut it off at the blue line I've added to this figure.
We don't apply the entire inviscid body's pressure distribution to the airfoil. We just apply the part we chopped off and kept.
Which leaves us with the problem -- we needed a full closed body's worth of pressures to cancel out and get to zero. What happens if we chop off a chunk and throw it away? I.e. we aren't dealing with a closed body?
Another way to think about it is to integrate the pressure on the outside of the boundary layer (without transferring it through to the airfoil). This integral would clearly need to extend to infinity to encompass the entire boundary layer.
Instead, when we cut it off at the blue line, and we do the integral around the BL near the airfoil -- but closed off by the blue line. What pressure do we apply along the blue line?
Since pressure is constant across the boundary layer, it will be the pressure at the outside of the boundary layer at the trailing edge.
The blue line is nearly vertical -- which means that any force we integrate across it will be in the thrust-drag direction.
Also, we know the pressure on this face (the pressure at the TE of the boundary layer). But we now see that the thicker the boundary layer, the longer the blue line. Consequently, the thickness of the boundary layer at the trailing edge is directly related to the amount of form drag.
From all this, we see that form drag is a pressure drag -- but it is a pressure drag that only exists because of viscous effects (the presence of the boundary layer).