We propose a combination of two dynamos for solar and stellar magnetic activity. A strong-field dynamo operating in the overshoot layer at the base of the convection zone generating superequipartition fields concentrated in isolated flux tubes is responsible for cyclic activity (e.g., sunspots), while a turbulent weak-field dynamo in the convection zone produces a more irregular field. The combination of a threshold in field strength for dynamo action due to instability of magnetic flux tubes in the overshoot layer and random fluctuations due to magnetic fields from the turbulent convection zone leads, in the case of the Sun and solar-type stars, to activity cycles with strong amplitude variations and the occasional appearance of grand minima. Stronger fluctuations may destroy the cyclic behaviour of the overshoot layer dynamo and lead to increased but irregular activity. Such activity is observed in fast rotating cool stars. On the other hand, stars with low and non-variable magnetic activity may be in a state with only the turbulent convection zone dynamo active.