We show that the synchronized states of two systems of identical chaotic maps subject to either, a common drive that acts with a probability p in time or to the same drive acting on a fraction p of the maps, are similar. The synchronization behavior of both systems can be inferred by considering the dynamics of a single chaotic map driven with a probability p. The synchronized states for these systems are characterized on their common space of parameters. Our results show that the presence of a common external drive for all times is not essential for reaching synchronization in a system of chaotic oscillators, nor is the simultaneous sharing of the drive by all the elements in the system. Rather, a crucial condition for achieving synchronization is the sharing of some minimal, average information by the elements in the system over long times.
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