FileInputStream vs FileReader

Yes, your conclusion is correct subclasses of Reader and Writer are for reading/writing text content. InputStream / OutputStream are for binary content. If you take a look at the documentation:

Reader - Abstract class for reading character streams

InputStream - Abstract class is the superclass of all classes representing an input stream of bytes.

FileReader (and indeed anything extending Reader) is indeed for text. From the documentation of Reader:

Abstract class for reading character streams.

(Emphasis mine.) Look at the API and you'll see it's all to do with text - char instead of byte all over the place.

InputStream and OutputStream are for binary data, such as mp4 files.

Personally I would avoid FileReader altogether though, as it always uses the system default character encoding - at least before Java 11. Instead, use InputStreamReader around a FileInputStream... but only when you want to deal with text. (Alternatively, use Files.newBufferedReader.)

As an aside, that's a very inefficient way of copying from an input to an output... use the overloads of read and write which read into or write from a buffer - either a byte[] or a char[]. Otherwise you're calling read and write for every single byte/character in the file.

You should also close IO streams in finally blocks so they're closed even if an exception is thrown while you're processing them.