Is there a difference between hierarchical GAM (HGAM) and Mixed effect GAM (GAMM)? What is the difference between Hierarchical GAMs (HGAM) and Mixed GAMs (GAMM), if any?
I am looking to model time series of count data against a range of candidate explanatory variables (hoping to understand which environmental parameters could explain the fluctuations). I have a year of data at 7 sites, quite different from each other in terms of environment, but not completely independent (species can easily move from one to another).
I struggle to identify which of the two frameworks would be the most appropriate. A HGAM with grouping per site, or a GAMM with site as a random variable... Is there any key difference I am missing here?
Thank you for any advice!

They are the same thing; we just prefer the terminology "hierarchical" over "mixed", because the salient practical feature of these models is that they can model variation in the response that occurs at multiple levels, rather than the fact that they have fixed and random effects.
