Generalized additive models vs. functional data models

Question

I am not sure I understand the difference between functional data analysis (FDA) and GAM. Or in short, I was reading about GAM and I found the following model which seems like an FDA model (there is a base function and its coefficients).

$$f(x) = \sum_{j=1}^q b_j(x) \gamma_j$$

Could you please help me understand what are the differences between the two methods?

UPDATE

From the discussions here and here it seems that someone can run all flavours of functional data analysis using GAM (or in brms). Also, this and this one give a short description of FDA vs traditional methods.

But still, I don't understand how the FDA is different from GAM.

Answer 1

By trying both methods for some time now I see that a main difference is that in FDA you actually get functional coefficients, meaning that your coefficients are depended on a particular moment of your continuum. So your covariates may have linear effect but you still can get a wiggly function. In contrast, with GAM you may fit a wiggly spline but you miss from interpretability.