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Practically speaking everyone knows what you're talking about regardless of the term you use, but you're not correcting anyone when you replace the more precise term microgravity with the less precise term zero-g.

The ISS is in free-fall around the earth but there is also a tiny amount of atmospheric drag and tidal effects from other bodies like the moon- it is not zero g.

https://en.m.wikipedia.org/wiki/Micro-g_environment

Gravimeters[1] are an incredibly cool technology. I'm given to understand that the most sensitive ones can actually track a person moving around the room it's in.

[1] https://en.wikipedia.org/wiki/Gravimeter

Yeah, and there's no known way to shield gravity so such a detector can see though walls.

You just need another person doing an offsetting walk on the opposite side of the sensor.

Not even by putting something of identical mass on other side of the detector?

Alternatively you could slow yourself down to absolute zero velocity such that you are no longer travelling through space, only time.

Is there a formal definition for those terms? Because there is some atmospheric drag at the ISS altitude, there is some tidal effect from it having finite size, and there is some manipulation even if only to keep it from hitting a wall.