A somewhat oversimplified, but useful distinction between concertato and concerto can be made: the concertato style involves contrast between opposing groups of voices and groups of instruments: the concerto style, especially as it developed into the concerto grosso later in the Baroque, involves contrast between large and small groups of similar composition (later called "ripieno" and "concertino").
The style developed in Venice in the late 16th century, mainly through the work of Andrea and Giovanni Gabrieli, who were working in the unique acoustical space of St. Mark's Cathedral. Different choirs or instrumental groupings occupied positions across the cathedral from each other: because of the sound delay from one side to the other in the large and acoustically "live" space, a perfect unison was difficult, and composers found that a fantastically effective music could be composed with the choirs singing across to each other, in stereo as it were; all accompanied by organ or other groups of instruments placed in such a way that they could hear each group equally well. Music written there was quickly performed elsewhere, and compositions in the new "concertato" style quickly became popular elsewhere in Europe (first in northern Italy, then in Germany and the rest of Italy, and then gradually in other parts of the continent). Another term sometimes used for this antiphonal use of the choirs in St. Mark's was cori spezzati. See also Venetian polychoral style and Venetian School.
In the early 17th century, almost all music with voices and basso continuo was called a concerto, though this use of the term is considerably different from the more modern meaning (a solo instrument or instruments accompanied by an orchestra). Often, sacred music in the concertato style in the early 17th century was descended from the motet: the texts that a hundred years earlier would have been set for a cappella voices singing in smooth polyphony, would now be set for voices and instruments in a concertato style. These pieces, no longer always called motets, were given a variety of names including concerto, Psalm (if a psalm setting), sinfonia, or symphoniae (for example in Heinrich Schütz's collections of Symphoniae Sacrae).
The concertato style made possible the composition of extremely dramatic music, one of the characteristic innovations of the early Baroque.