  The possibility for detuned spins to display synchronous oscillations in
local observables is analyzed in the presence of collective dissipation and
incoherent pumping. We show that there exist two distinct mechanisms that can
give rise to synchronization, that is, non-degenerate subradiance and
coalescence. The former, known as transient synchronization, is here
generalized in the presence of pumping. It is due to long-lasting coherences
leading to a progressive frequency selection. In the same set-up, even if under
different conditions, coalescence and exceptional points are found which can
lead to regimes where a single oscillation frequency is present in the relevant
quantities. Still, we show that synchronization can be established only after
steady phase-locking occurs. Distinctive spectral features of synchronization
by these two different mechanisms are reported for two-time correlations.
