Did a bit of research.
It's pretty clear what the tangent line is:
So you have a curve which is produced by some function. You choose a point on the curve. And you draw a line tangent to it.
To calculate that line position you get the derivative of the curve function.
By extrapolating 2D curve to 3D surface you can get the idea of what the tangent plane is. And there are formulas to calculate that plane in a specified point of the surface.
Now the term "surface to surface tangency". I don't get it. Is it a plane that is tangent to both surfaces? Does it mean surfaces need to intersect? Is it a curve that is a result of 2 surfaces intersecting? Or is it just a point where two surfaces touch?
Is there a picture that describes what you want?