The file manager that comes with elementary OS is unusual when compared to those in other Linux desktop environments. It has the typical file listing preferences of most other file managers but it also has the option to view contents as columns. You click on a folder, and it shows the folders inside that one in the first column. Then you click on another folder and it shows its contents in the next column and so on.
The attached screenshot explains it better. I'm hoping the Macheads can weigh in on this. Is this similar to how the file manager works in Mac OS? In any case, I like it.
Yes, it is similar, and I like it better than Gnome Files. I'm unhappy with Gnome Files right now, as the newest version doesn't have column views (yet) and the spacing of icons in List View and Grid View is ridiculously large.
I wish I knew the name of it and then maybe you could find it elsewhere and perhaps install it under Gnome. As you can see in the screen capture, there is no drop-down menu or 'about' button. It doesn't have this feature, but you could look at installing the Plasma file manager, Dolphin. It would have to likely install some Plasma base files but it might be worth it. It has a lot more features than the Gnome file manager. You can use Timeshift to make a system image before you install it in case it messes up your distro.
I like Dolphin - Mint and Kubuntu use it.