Yes, there are an infinite number of ways to compute the finite value of \$R=300\:\Omega\$. However, you are actually computing \$R=\frac{V_\text{CC}-V_\text{LED}}{I_\text{LED}}\$. And there is only one way to calculate that in your example case:

$$R=\frac{V_\text{CC}-V_\text{LED}}{I_\text{LED}}=\frac{9\:\text{V}-3\:\text{V}}{20\:\text{mA}}=300\:\Omega$$

Note that for any given voltage source, \$V_\text{CC}\$, and for given values for the LED, you get exactly one way to calculate the resistor's magnitude.

The reality is a little more complex. LEDs vary, one from another, with no two of them exactly alike. The datasheets will specify a range of voltages that may be exhibited by any specific LED (of the same type and manufacture) when a certain current flows through it. This can be quite a range, too. So the value you use for \$V_\text{LED}\$ will only ever be an approximation/average value. You could use the equation with the upper and lower limits and get two different values for \$R\$ and then decide if you want to pick from one or more standard values within that range.