Burn rate for black powder depends on particle size. Fine powder burns faster than coarse powder. So one characteristic of high-quality powder is uniform particle size.

But yes, changing the formulation also affects burn rate. For example, replacing potassium nitrate with potassium perchlorate yields a much faster burn.[0] Also replacing the carbon with aluminum dust gives you flash powder.[1]

0) https://pyrodata.com/compositions/Black-Powder-Perchlorate

1) https://pyrodata.com/composition/flash-powder