Black smoke is soot. Common when accelerating as extra fuel is injected. More common on engines more than a few years old, newer ones are generally better, not due to lower age, but better controlled fuelling. Black smoke is the result of less efficient combustion.
Blue smoke is oil, which would show poor engine condition, or leaking turbo seals.
White(light grey) smoke is unburnt fuel. Sometimes present at startup on cold days. Other times indicates poor combustion, or excess fuel, more than the air can burn.
If your black smoke is only on acceleration, get a good quality injector cleaner, like Forte or Wynns and dose it. Cleaner injectors may well cure it. Otherwise, if it goes ok, sounds ok and fuel consumption is ok, don't fret.