We analyzed and compared the seismic activity that has occurred in the last two to three decades in three distinct volcanic areas: Phlegraean Fields, Italy; Vesuvius, Italy; and Long Valley, California. Our main goal is to identify and discuss common features and peculiarities in the temporal evolution of earthquake sequences that may reflect similarities and differences in the generating processes between these volcanic systems. In particular, we tried to characterize the time series of the number of events and of the seismic energy release in terms of stochastic, deterministic, and chaotic components. The time sequences from each area consist of thousands of earthquakes that allow a detailed quantitative analysis and comparison. The results obtained show no evidence for either deterministic or chaotic components in the earthquake sequences in Long Valley caldera, which appears to be dominated by stochastic behavior. In contrast, earthquake sequences at Phlegraean Fields and Mount Vesuvius show a deterministic signal mainly consisting of a 24-hour periodicity. Our analysis suggests that the modulation in seismicity is in some way related to thermal diurnal processes, rather than luni-solar tidal effects. Independently from the process that generates these periodicities on the seismicity, it is suggested that the lack (or presence) of diurnal cycles in seismic swarms of volcanic areas could be closely linked to the presence (or lack) of magma motion.