E-book is short for "Electronic Book" as far as I know it is a generic term and not a trade mark
I have the KINDLE for Windows 8 app on this beast and KINDLE FOR PC on my older XP machines, Kindle for Android on my phone and yes there is one for IOS as well.
All these apps are free to download from Amazon kindle store.
A book once downloaded is also posted to your cloud account, along with some tags (Current position for example) so you can open a book on your PC read a while.... Then close, Go shopping with the darling spouse, And while waiting open the Kindle app on your phone, pick up right where you left off,,, Then close it and return to the PC.
You can also E-Mail your kindle some file types. (.PDF, .MOBI .TXT and a few others) and they too will pop into (I am told) the cloud account so you can read on everything.
By the way.. I did most all of this ... TODAY.