This is a great question. Fortunately it has a very simple answer, which has the added benefit of being mostly true! They are different iterations of the same thing over time. You can think of the Pyramid Texts^(1,2,3) as being Old Egyptian from the Old Kingdom, Coffin Texts^(4) as Middle Egyptian from the Middle Kingdom, and the various "Books of the Dead" as Middle Egyptian from the New Kingdom onward until the end of the Pharaonic Period.
That's the general thrust. There are a few wrinkles in there. Most notably, the New Kingdom funerary texts include much more than the text known as the "Book of the Dead" colloquially. That one is usually The Book of Going Forth by Day,^(5) but you could also add the Amduat,^(6) The Book of Gates,^(7) and a handful of others that were less frequently copied. You might have noticed that I said Middle Egyptian from the New Kingdom for the Books of the Dead. That's because Middle Egyptian became the prestige language of ancient Egyptian, much like Latin in Medieval Europe. Middle Egyptian was used to write certain high-register texts long after it was no longer the spoken language, including the Books of the Dead.
There are differences between them of course. It was an ongoing tradition with new things being added and subtracted over time. The main trend overall was a movement toward universality. The Pyramid Texts were probably only for kings and some queens. The Coffin Texts were accessible to the elite who could afford finely crafted coffins with inscribed texts. The later Books of the Dead were available to pretty much anyone who could afford to buy a papyrus. They were still quite expensive, but a motivated person of any social class might be able to save up for one.
For a thorough but accessible overview, which won't require you to read Egyptian, check out Following Osiris^(8) in the sources below.