Panel data is defined in wikipedia as:
In statistics and econometrics, panel data and longitudinal data are both multi-dimensional data involving measurements over time. Panel data is a subset of longitudinal data where observations are for the same subjects each time.
While functional data is defined as:
Functional data analysis (FDA) is a branch of statistics that analyzes data providing information about curves, surfaces or anything else varying over a continuum.
As far as I read, it is common to consider time as the continuum over which FDA data varies. And methodologies in FDA seem to work by "projecting" the infinite dimensional space of time into a finite dimensional space that yields to a multivariate problem.
So how is then FDA different than panel data?