The Unicode Normalization FAQ includes the following paragraph:
Programs should always compare canonical-equivalent Unicode strings as equal ... The Unico
NFC is the general common sense form that you should use, ä
is 1 code point there and that makes sense.
NFD is good for certain internal processing - if you want to make accent-insensitive searches or sorting, having your string in NFD makes it much easier and faster. Another usage is making more robust slug titles. These are just the most obvious ones, I am sure there are plenty of more uses.
If two strings x and y are canonical equivalents, then
toNFC(x) = toNFC(y)
toNFD(x) = toNFD(y)
Is that what you meant?