Well if Type means anything, changing Type should then remove any and all characteristics associated with Type. If you are no longer a Fiend, you should lose all powers associated with being a fiend. The rules specifically say there are no rules associated with Type, but there's a certain amount of "It stands to reason..." here.
In the end, if the thing is still filled with the magic and energies of a fiend, it should probably still detect as one.
I get what you're saying. If Durin's Bane takes on the form of an elf maiden, he's still a balrog, a demon, and a fiend on the inside.
But there are no characteristics associated with type. AFAICT, there isn't any single quality all fiends have in common, so none of a creature's particular characteristics, other than its creature type, are what makes it a fiend.
The spell
shapechange (v5.0) is specific about what characteristics port over to the new form. You keep your alignment, Intelligence, Wisdom, and Charisma scores, skill and save proficiencies, and the benefit of any features from your class, race, etc. but not any special senses.
So let's say a balor is somehow shapechanged into an elf. What we have now, assuming the balor is typical, is a chaotic evil elf with an Intelligence, Wisdom, and Charisma of 20, 16, and 22 respectively (not unheard of for an elf), proficiency with Str, Con, Wis, and Cha saves, the damage resistances and damage and condition immunities of a balor, and the ability to speak Abyssal and use telepathy, that explodes when it dies, has a fire aura and magic resistance and weapons, and can multiattack and teleport. Now which of these characteristics are the characteristics of a fiend? Cold resistance and telepathy are fairly common among fiends but are nowhere near universal in creatures with the fiend creature type so cannot be said to be characteristics that are intrinsic to fiends because there are no such characteristics. The closest is evil alignment, but alignment itself as a statistic is only an indicator of what's typical and varies from individual to individual.
All this being said, I've blundered in bringing up
shapechange at all. It appears the OP was attempting to discuss the night hag action Change Shape, so I apologize for inadvertently derailing the thread and will address the night hag feature in a separate post.