Hi,
A lot of the possible confusion arises due to the fact that accelerometers don't measure acceleration - they measure a force and divide that force by a mass to get a result that has the units of acceleration.
Consider an accelerometer that contains a magnet of mass m. It has coils to produce a magnetic field, and by controlling the currents in those coils, it can control the position of the mass within itself. It's control system is designed to keep the magnet levitating at a fixed position within it. (Note that that isn't the type of accelerometer you are likely to be using - but it may help with understanding).
If you place the accelerometer on the desk in front of you, an apparent weight force mg (where g has the units of acceleration, but is really a conversion factor to convert from mass to apparent weight force magnitude, and which varies with geographical position and height above the ground) acts vertically downwards on the mass. The control system has to produce an upwards force of magnitude mg to counteract it. It divides that by m, and therefore gives an output "acceleration" of g vertically downwards (although some accelerometers are calibrated to give zero output in that situation - i.e. they subtract it from the measured value before outputting the result).
If the accelerometer is attached to something that is "accelerating vertically downwards" at 2 m/s^2, for example, then the control system will have to apply a lower force upwards on the mass to keep it in position within the accelerometer. The upwards force will be m(g-2), and so it will give an output of (g-2) upwards.
All acceleration is relative - it depends on what you measure it relative to. I appear to be fairly static as I type this to someone looking in my window, but, if observed by someone at the centre of the Earth, for example, we are both accelerating towards the axis of rotation of the Earth (that's what keeps us rotating with the Earth). That acceleration is not g - it's much lower, and depends on where you are - for example, it's zero at the poles.
The actual net gravitational force acting on me due to the gravitational interaction between my matter and that of the Earth is different to the apparent weight force acting on me. The apparent weight force (mg acting vertically downwards) is adjusted to take into account the fact that I'm accelerating towards the axis of rotation of the Earth - the value of the conversion factor g takes it into account when calculating the magnitude of the force, and the direction "vertically downwards" also takes it into account.
The fact that acceleration is relative, and the fact that my actual acceleration, measured from, for example, the centre of the Earth (or from, for example, some fixed point in space), has a different magnitude and direction to the acceleration of other people in other places, complicates things. That's why simplifications are made. So, we often consider a person standing still on the Earth to be "static", and that the acceleration of an object relative to them is the object's "acceleration". The value of g is adjusted to make that possible (and "vertically downwards" changes with location). That's fine for most things you need to deal with - but falls apart when you start thinking about the ISS, for example.
Don't know if that clarifies anything really!
All the best,
Alan
