  Photon correlations, as measured by Glauber's $n$-th order coherence
functions $g^{(n)}$, are highly sought to be minimized and/or maximized. In
systems that are coherently driven, so-called blockades can give rise to strong
correlations according to two scenarios based on level-repulsion (conventional
blockade) or interferences (unconventional blockade). Here we show how these
two approaches relate to the admixing of a coherent state with a quantum state
such as a squeezed state for the simplest and most recurrent case. The emission
from a variety of systems, such as resonance fluorescence, the Jaynes-Cummings
model or microcavity polaritons, as a few examples of a large family of quantum
optical sources, are shown to be particular cases of such admixtures, that can
further be doctored-up externally by adding an amplitude- and phase-controlled
coherent field with the effect of tuning the photon statistics from exactly
zero to infinity. We show how such an understanding also allows to classify
photon statistics throughout platforms according to conventional and
unconventional features, with the effect of optimizing the correlations and
with possible spectroscopic applications. In particular, we show how
configurations that can realize simultaneously conventional and unconventional
antibunching bring the best of both worlds: huge antibunching (unconventional)
with large populations and being robust to dephasing (conventional).
