The first appearance of pieces exhibiting the title "concerti" are by Andrea Gabrielli from 1585, and might be described as Masses for voices that are organised into antiphonally organised groups such that their contrasting timbres and musical characters form the main thrust of the work.
That only some of the voices are marked "a cappella" suggests that the other "choirs" are actually played by instrumental ensembles. Thus the earliest use of "concerto" suggests, simply, voices and instruments.
Ten years later the Bolognese organist Adriano Banchieri's piece Concerti ecclesiastici a otto voci was published including a seperate part for the organist that contained a harmonic "reduction" of the many vocal and instrumental parts. Accompanied songs soon after were published with an even more streamlined organ part, called the basso continuo.
The basso continuo was not "invented" at this time. Simply, publishers were now documented a practice that organised had long used in their "oral" tradition.
Interestingly, this new development gave rise to backlash among some organists who saw the published, "fully-realised" basso continuo part as an easy way for the lazy to play something that previously only the studied could.