From 150 Questions about the Psalter by Bradley Johnston:
Q13. Why does the Apostle Paul use the words 'psalms and hymns and songs' to teach the churches about singing?
A. The Apostle Paul uses the three words 'psalms and hymns and songs' to teach the churches about singing because they were featured in the Greek Old Testament (LXX) used by his original readers. The inscriptions of the Greek Psalter use 'psalm' 67 times, 'hymn' 6 times, and 'song' 36 times. All three words are used repeatedly in the text of the Psalter itself.
For a more in depth treatment of this subject, consider reading the RPCNA Report on Psalmody in the Church (accessible here)