A sourdough culture will always contain one or more species of yeast. In some cases these yeasts might even include the same species (Saccharomyces cerevisiae) that is sold as bakers’ and brewers’ yeast.
So the answer is no.
That said, the strains of S. cerevisiae found in bakers’ and brewers’ yeast have been modified of years of selective breeding (for example to produce large volumes of carbon dioxide/alcohol, respectively, and to generate different flavour profiles in the finished product), perhaps even by genetic modification in some cases. It is unlikely that even if S. cerevisiae is present in a sourdough culture that it will be genetically identical to a commercial strain.
Concentrations of yeast in a genuine sourdough may well be lower than in a bread made with commercial yeast. Rather than using a relatively large amount of yeast cells to produce the amount of carbon dioxide needed over a relatively short period of time, sourdough relies upon its smaller number of yeast cells being left for a longer fermentation period to generate the same amount of gas.