The titles of the Psalms in the Septuagint are as follows:

ψαλμος (3-9, 11-15, 19-25, 29-31, 38-41, 43-44, 46-51, 62-68, 73, 75-77, 79-85, 87-88, 92, 94, 98-101, 108-110, 139-141, 143)

συνεσιν (32, 42, 44-45, 52-55, 74, 78, 88-89, 142)

υμνοις (6, 54-55, 61, 67, 76)

ωδη (4, 18, 30, 39, 45, 48, 65-68, 75-76, 83, 87-88, 91-93, 95-96, 108, 120-134)

Paul's terms for the Psalter are:

In Colossians 3:16:
1. ψαλμοις
2. υμνοις
3. ωδαις πνευματικαις

In Ephesians 5:19:
1. ψαλμοις
2. υμνοις
3. ωδαις πνευματικαις

Colossians 3:16 ο λογος του χριστου ενοικειτω εν υμιν πλουσιως εν παση σοφια διδασκοντες και νουθετουντες εαυτους ψαλμοις και υμνοις και ωδαις πνευματικαις εν χαριτι αδοντες εν τη καρδια υμων τω κυριω

Ephesians 5:19 λαλουντες εαυτοις ψαλμοις και υμνοις και ωδαις πνευματικαις αδοντες και ψαλλοντες εν τη καρδια υμων τω κυριω

It would be reasonable, with the Westminster Divines, to conclude that Paul was not referring to un-inspired songs, nor inspired words not commanded to be sung, but to the divinely inspired Psalter, as translated into the Greek Septuagint.