Reynolds number determines turbulent or laminar but Moody Chart has different interpretation

Yes, Reynolds number is enough. In circular pipes:

$Re = frac{rho V D}{mu} = frac{V D}{nu}$

As you pointed out, the flow becomes turbulent at about $Re = 4000$. For values lower than $2100$ it is laminar. For values in between is transitional. This is seen in the typical experience in a stream of dye injected in the direction of the pipe flow. If the flow is laminar, you will see a straight line of dye. If it is transitional, the line of dye will have fluctuations (in space and time) and will start showing eventual bursts of irregular behaviour. If the flow is turbulent, you will see the dye being spread and blurred randomly in space and time.

Let's say that we are now in turbulent regime.

Now we can look into the dashed line called in that figure "Complete Turbulence".

What happens if the Reynolds number is small enough (but still turbulent $> 4000$) and roughness is also small enough is that, in a thin layer next to the wall, the flow is dominated by viscous effects (viscous sublayer).

When Reynolds increases, the thickness of this layer decreases. So, if the Reynolds is high enough (layer getting very thin) and the roughness gets very large (big microscopic features), there is no thin viscous layer anymore and the near wall region is dominated by the surface roughness features. This corresponds to the "Complete Turbulence" in the Moody chart (horizontal lines in the plot - independence from $Re$ - region to the right of the dashed line).

So, as pointed out in other comments, there are two "transitions". One is between the transitional flow and turbulent flow (just ignoring laminar for this discussion) and it occurs roughly at $Re = 4000$. The other occurs within the domains of the turbulent regime, and has to do with the transition between a near wall region dominated or not by viscous effects.

Note that, at $Re = 10000$ (your example), whether you are to the left or to the right of the dashed line, you are still in turbulent regime.

There are actually two "transitions," one from laminar to turbulent flow, and the other from "smooth wall turbulence" to "full turbulence." So there is actually no ambiguity with regard to the transition from laminar to turbulent flow.