A digital receiver decides which symbol or bit was transmitted from a noisy observation.

The symbol error probability is

$$P_s=\Pr(\hat S\ne S),$$

where $S$ is the transmitted symbol and $\hat S$ is the receiver decision.

The bit error probability is

$$P_b=\Pr(\hat B\ne B).$$

In measurements or simulations, the corresponding error rates are estimated by counting errors over many transmitted symbols or bits, for example

$$\widehat{P_b}=\frac{N_{\text{bit errors}}}{N_{\text{transmitted bits}}}.$$

Symbol and bit error are not generally the same. One wrong $M$-ary symbol can change several represented bits, and the mapping between bit patterns and constellation points affects how many bit errors a symbol decision causes.

Error probability is a receiver-performance metric. It must always be interpreted together with the channel model, modulation, coding and operating conditions under which it was obtained.