I am trying to think up a word that I recall existing for a linguistic idea that I just cannot recall the name of.
It is the idea of when you take a big group and refer to the entire group by the name of one component of it. Such as an old man calling all video games "Nintendos", or calling all birds "chickens"
Can anyone remember what the name of this process is?
There are several terms for various aspects of this phenomenon.
The overarching term is metonymy, which is just referring to something by a name closely connected to the thing (in some way).
More specifically, referring to a larger concept or group by the name of a subsection or individual entity within that concept is known as synecdoche, more specifically as pars pro toto (‘a part for the whole’). Synecdoche can also refer to the opposite, totum pro parte (‘the whole for a part’).
Other related concepts are merisms, meronymy and holonymy, hyper- and hyponymy, etc.
