I understand that most people view these as being the same thing, but I have put a lot of thought into the differences between the two. In point of fact, I have wanted to change shape since I was in my early teens and my eldest sister handed me a syfy/fantasy book with a shapechanger in it. Being that I am now two years away from my sixtieth year that is a fairly long time to consider the subject even with large gaps where I thought about many other this.
Recently there have been many movies and books with Werewolves being the main characters. Some stick to the belief that Werewolves must be bitten by another Were in order to shift into wolf form (or partial wolf form) on nights of the full moon. Another, very popular series shows the shifting as being inherited and can be done at will. Either way the shift only allows for the human form and one other, whether that be in the form of a wolf or bear or whatever the virus allows. The Native Americans called this Skinwalking, and incorporate into that belief the fact skinwalkers aquire the ability either by being bitten or through dark shamanism. Again, either way there is only the one shape besides human. To me, that is Shapeshifting.
There are also stories and movies lately with Shapechangers in them, but not nearly as many. Shapechangers are not limited to just one form beyond human, but can change into any creature (large or small) they wish, although inanimate objects are harder to achieve, this can also be done with practice. This is done, not through a virus, but through the DNA. It is an ability people are born with, although not everyone can activate that change. Many of the dragons of old were shapechangers and came among Mankind as teachers and friends, unlike their Creature born cousins the fire breathing dragons, both of which had to either hide or flee the Earth when Mankind turned against them. Yes, I know I write that as if it were true, and who knows, maybe it is and perhaps you, yourself, have a bit of shapechanger dragon blood within you.
In my book Annie's Trail there are shapechangers, more and more each generation upon the planet Vardes due to the mutations occurring in the DNA of the humans who colonized the world. On that world some are born instinctively knowing how to change their shapes, while others find the ability when they are faced with intense emotions. Either way, they are changers, not shifters, because the virus which caused the Weres of our legends (?) never migrated with them to this new and very much aware planet.
Anyway... those are my thoughts about the differences between "shifting" and "changing". I'd love to hear other opinions on the subject if you choose to give me some :) hugs and thanks for taking the time to read this :)