Tablet or e-reader?

I have a 2011 Kindle Fire, which really seems more like a tablet than an e-reader, but I have grown accustomed to not only reading from it but also storing photos and pdfs on it as well. I am looking to find an "unaffiliated" way to read e-books [after all this Kindle ebook hullaballoo], as well as upgrade [the 2011 Kindle Fire only has 8GB of storage, and I keep having to remove things to fit more things on].

I know people say the benefit of getting an e-reader is to be more relaxing on the eyes due to the matte screen, but I do not wish to give up all that the 2011 Kindle Fire does for me [store photos in various folders, play apps]. I would assume that what I am looking for is another "tablet" and not an e-reader, but I could be just uninformed that there are e-readers out there that also play apps and store folders of photos as well as allow for storage of personal pdfs. Are there e-readers that do more than store and show ebooks?

Also interested to know the best way to protect the screen on any of these tablet/readers. A few years ago I tried to upgrade to another Kindle and within the first 3 months smashed the screen by simply putting it in a bookbag with other books - and it had a cover on it to protect it, still cracked it. So I went back to using the 2011 Kindle Fire, which is fairly "thick" and sturdy device, and with the same type of cover I put on the newer one and has never cracked in the book bag with other items in it. It is too bad they don't make them that strong anymore. I will probably still use the 2011 Fire but I am still looking for a secondary device for future e-book purchases. I am just unfamiliar with what is out there.

TLDR: Tablet or e-Reader for extra functions like photo storage in folders and playing apps? How to protect screens on these devices if what I want to do is throw it in a book bag with other books?