If you use the remove "from device" option it basically archives the book (deletes the kepub file from the file system on the device) but it keeps a reference in the app, which visibly appears as the book cover image. It puts the book into a non-downloaded state too, so in the bottom right hand corner of the cover image there should be a circular download icon.
This option only removes it from that single device. The "from library" option deletes the book from the device and the library, which equates to the web site's "I'm Reading" list, and that is what all the apps / devices use as the master list of books that will be displayed on a device or in the apps.
I'm trying to remember the logic surrounding what the home screen displays, as in downloaded vs non-downloaded items. I can say for certain that at present you cannot remove a home page tile on iOS.
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