Is there an easy way of listing files in different folders to transfer from one window to another

I saw this feature on a very elderly Mac machine but thought it was really very useful: two windows side by side each showing the contents of a folder or USB drive so that you can move files from one to another. There must be some way of doing something similar in Ubuntu. I tried simply having two nautilus windows open alongside each other, but it's really very clunky.

It looks that you are looking for a twin-panel file manager, also called sometimes a commander (from the name of the first program with this kind of interface, Norton Commander for DOS, released in 1986 !).

There are several you can choose from. You didn't specify which Ubuntu version do you use, but in 20.04 directly from Ubuntu's Snap Store you can install Double Commander, Tux Commander, Midnight Commander, Krusader or Worker. All have similar basic features (although differ in more advanced ones), so visual appearance will be probably the main factor in choosing one or the other.

Double Commander and Tux Commander are probably the "nicest" ones, the first of them being more "fancy" and the second having much simpler, "cleaner" interface - some people might prefer that (look at the screenshots below).

Krusader is designed for KDE, so if you try to install it under GNOME, it will pull in a large part of KDE run-time libraries with it. While this should work, myself I would rather avoid installing KDE-dependent software under GNOME to keep the system "clean".

Midnight Commander is a "classic"; it runs in text mode, so if you often use the terminal (for example you are connecting via ssh to your machine), it is a "must have" tool.

Worker is the most ugly one; its interface looks messy and I wouldn't recommend it.

Here are screenshots of all of them, except Krusader:

Double Commander (I have changed the default icon size in the settings from 32x32 to 16x16 - which I recommend - to get more compact file list display in the panels):

Tux Commander:

Midnight Commander (inside a GNOME terminal window):

Worker:

caja (the default gui file manager in Ubuntu MATE) supports this; press F3 or go to View → Extra Pane and you will get