Is mg/m^3 same as ppmw (CO2)?
No. ppmw means parts per million by weight (mass). This is not the same as mg/m3, which is milligrams (mass) per cubic meter (volume).

For example, in a gas of very low density (e.g. $\ce{CO2}$ at 10-6 Pa), 1 mg/m3 could exceed the weight of $\ce{CO2}$, i.e. would be greater than 900,000 ppmw.

One measure has to do with mass in a given volume, the other measure is mass in a given mass of another substance.