The term seconda pratica first appeared in 1603 in Giovanni Artusi's book Seconda Parte dell'Artusi, overo Delle imperfettioni della moderna musica (The Second Part of The Artusi, or, Imperfections of Modern Music), where it is attributed to a certain L'Ottuso Accademico.
In the second part of this work, L'Ottuso Accademico, whose identity is unknown, defends Monteverdi and others "who have embraced this new second practice".
[1] Monteverdi adopted the term to distance some of his music from that of e.g. Giovanni Pierluigi da Palestrina and Gioseffo Zarlino and to describe early music of the Baroque period which encouraged more freedom from the rigorous limitations of dissonances and counterpoint characteristic of the prima pratica.
Stile moderno was coined as an expression by Giulio Caccini in his 1602 work Le nuove musiche which contained numerous monodies.
Also this marks the starting point of basso continuo which also was a feature in Caccini's work.