Question: If acceleration of something $= - 10 \text{ m s}^{-2}$

And forwards is define as north. 

Does that mean the object is getting slower (decelerating) or accelerating in the reverse direction (south)

How can you tell the difference?

Answer: 
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> Does that mean the object is getting slower (decelerating) or accelerating in the reverse direction (south)
> 
> 
> 

It *really* doesn't matter. Basic kinematic formulas are designed to work just as well in either case, which is why physicists don't generally use the word "decelerating." It's just another kind of acceleration.

That being said, if you want to determine whether the object's *speed* is increasing or decreasing (which correspond to the popular meanings of "accelerating" and "decelerating" respectively), you can just look at the orientation of the acceleration with respect to the velocity. If the acceleration is parallel to the velocity, the object will be speeding up. If it's antiparallel, the object will be slowing down. You can see this mathematically by taking the derivative of the kinetic energy:

$$\frac{\mathrm{d}}{\mathrm{d}t}\biggl[\frac{1}{2}mv^2\biggr] = m\vec{v}\cdot\frac{\mathrm{d}\vec{v}}{\mathrm{d}t} = m\vec{v}\cdot\vec{a}$$

So the sign of the dot product $\vec{v}\cdot\vec{a}$ tells you whether the speed is increasing or decreasing.

Do note that velocity is reference frame-dependent. So two different inertial observers looking at the same object at the same time could have differing conclusions as to whether it is speeding up or slowing down. That's one big reason why the distinction is not important in physics.
The answer depends entirely on what you define as stopped{\*}.

Moreover, physics must be the same in all inertial reference frames{+}, which means that it can not depend on the distinction you are trying to make.

Accordingly there is no physical difference, just a linguistic one that relies on a common understanding of "stopped".

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{\*} Growing up on the surface of a planet with a non-trivial atmosphere you are probably used to thinking of the frame of the ground as special for these purposes, but physics doesn't believe in that.

{+} The principle of relativity.