A BJT is commonly analyzed using three operating regions.

In cutoff, both junctions are effectively not forward biased and the collector current is small.

In forward active, the base-emitter junction is forward biased and the base-collector junction is reverse biased. This is the region used for linear amplification. A simple model uses

$$I_C\approx \beta I_B$$

or, more accurately for voltage-controlled analysis,

$$I_C\approx I_S e^{V_{BE}/V_T},$$

where $V_T$ is the thermal voltage.

In saturation, both junctions are forward biased. The transistor is strongly on, but the relation $I_C=\beta I_B$ no longer describes the collector current. A circuit model often approximates the collector-emitter voltage by a small saturation voltage $V_{CE(sat)}$.

These regions play different roles: cutoff and saturation are useful for switching, while forward active provides the controlled current relation used in analog amplification.