I'm answering your initial question directly, but there is more going on that may be more informative.
This is a distinction between computation that is performed on a server, using arbitrary tools, and computation run on a user's machine locally. The former is much more flexible, but comes at a cost of latency; all user input and output must be serialized, and transmitted a long distance. Front end code can result in much lower latency to the user due to ommitting this transmission.
It makes sense to apply a suitable mix of these two tools that varies based on an application's details. For example, an immediate UI response that can be performed using only information already present on the client makes sense to be handled exclusively there, as computation time is minimal compared to transmission and serializtion.
I believe that JS being able to be used on a server is not relevant to the core distinction.
Though, as most apps are built, only the code run on the server can be trusted, and only the response processing performed on the server can be trusted.
This is a distinction between computation that is performed on a server, using arbitrary tools, and computation run on a user's machine locally. The former is much more flexible, but comes at a cost of latency; all user input and output must be serialized, and transmitted a long distance. Front end code can result in much lower latency to the user due to ommitting this transmission.
It makes sense to apply a suitable mix of these two tools that varies based on an application's details. For example, an immediate UI response that can be performed using only information already present on the client makes sense to be handled exclusively there, as computation time is minimal compared to transmission and serializtion.
I believe that JS being able to be used on a server is not relevant to the core distinction.