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Because calling it a four thirds sensor would just confuse the matter, given that you can't mount a micro four thirds lens to a four thirds lens mount camera body, despite them both using four thirds sensors.
The people that need to know the difference already know the difference, and the people that don't know the difference are really talking about lens compatibility and not sensor size.
I don't see how it would be confusing when not all mirrorless cameras with 4/3 sensors are even compatible with mft. It has caused me quite a bit of confusion and videos explicitly talking about image sensors are mixing them up.
Agree. People talk about full frame and APS-C sensors independently of whether that sensor is in a DSLR or MILC body.
One possible explanation is that some FF and APS-C DSLRs are still in production while four thirds DSLRs stopped production 15 or so years ago. Four thirds also doubles as the name of the first system, which helps add to the confusion.
I don’t see how it would be confusing when not all mirrorless cameras with 4/3 sensors are even compatible with mft
That's my point. If you see someone saying "micro four thirds" what they really mean "micro four thirds lens mount on a four thirds sensor"
No one is talking about four thirds lens mount systems anymore, because it's a deprecated format
As far as I know, the "four thirds" mount was an open, with the same sensor size as its successor, the "micro four thirds" mount. The former was a DSLR system, the latter is a mirrorless system. I don't think there are any commercially available interchangeable lens cameras with that aspect ratio, that don't use either of the two standard mounts - they are both from the Micro Four Thirds Standard Group (link).