How does it regulate "spiritual songs" though, as there are many worship songs performed that are spiritual in meaning/terminology?
I think, exegetically, that spiritual refers to all three. Also, it would best be seen as Psalms, Hymns, and Songs of the Spirit (inspired). That's my take, and others as well.
Here are some others who have commented on these passages:
John Calvin: “Now St. Paul sets down here songs, psalms, and hymns, which scarcely differ at all from one another, and therefore there is no need to seek entertainment for ourselves in setting forth any subtle distinction among them.”(Sermons on Ephesians (5:18-21), pp. 552-553)
John Cotton (1584-1652), New England Congregationalist theologian: “In both which places (Eph. 5:19, Col. 3:16), as the apostle exhorteth us to singing, so he instructeth us what the matter of our song should be, to wit, Psalmes, hymnes, and spirituall Songs. Now these three be the very titles of the Songs of David, as they are delivered to us by the Holy Ghost himself: some of them are called Mizmorim, that is Psalmes; some Tehillim, that is Hymnes; some Shirim, that is Songs, spirituall Songs. Now what reason can be given why the apostle should direct us in our singing to the very titles of David’s Psalms, if it were not his meaning that we should sing them? … The words of David and Asaph, as they were the words of Christ in the mouth of David and Asaph: so they were the words of Christ also in the mouths of the sonnes of Corah, or any other singers in the Temple.”
David Dickson: “The reason of the Precept is from those better fruits which spiritual joy produceth, such are all sorts of spiritual Songs, especially those which are in the holy Scriptures, with which they should mutually edifie one another, and glorifie God from their heart or spiritual affection. A Psalm is a sacred song in general, especially that which is by playing on the harp. A Hymn properly contains Gods praise. An Ode or Song, is a common name.”(Commentary on Eph. 5)
John Gill: “By psalms are meant the Psalms of David, and others which compose the book that goes by that name, for other psalms there are none; and by “hymns” we are to understand, not such as are made by good men, without the inspiration of the Spirit of God; since they are placed between psalms and spiritual songs, made by men inspired by the Holy Ghost; and are put upon a level with them, and to be sung along with them, to the edification of churches; but these are only another name for the Book of Psalms, the running title of which may as well be the Book of Hymns, as it is rendered by Ainsworth; and the psalm which our Lord sung with his disciples after the supper, is called an hymn; and so are the psalms in general called hymns, by Philo the Jew; and songs and hymns by Josephus; and, “songs and praises”, or “hymns”, in the Talmud: and by “spiritual songs” are meant the same Psalms of David, Asaph and the titles of many of them are songs, and sometimes a psalm and song, and song and psalm, a song of degrees; together with all other Scriptural songs, written by inspired men; and which are called “spiritual”, because they are indited by the Spirit of God, consist of spiritual matter, and are designed for spiritual edification; and are opposed to all profane, loose, and wanton songs: these three words answer to the several titles of David’s Psalms”(Commentary on Eph. 5)
Matthew Henry: “We must admonish one another in psalms and hymns. Observe, Singing of psalms is a gospel ordinance: psalmois kai hymnois kai odais—the Psalms of David, and spiritual hymns and odes, collected out of the scripture, and suited to special occasions, instead of their lewd and profane songs in their idolatrous worship. Religious poesy seems countenanced by these expressions and is capable of great edification. But, when we sing psalms, we make no melody unless we sing with grace in our hearts, unless we are suitably affected with what we sing and go along in it with true devotion and understanding. Singing of psalms is a teaching ordinance as well as a praising ordinance; and we are not only to quicken and encourage ourselves, but to teach and admonish one another, mutually excite our affections, and convey instructions.”(Commentary on Col. 3)
Thomas Manton (1620-1677): English Puritan, commenting on Ephesians 5:19: “The learned observe, these are the express titles of David’s Psalms, mizmorim, tehillim, and Shirim, which the Septuagint translate, psalmoi, humnoi, and odai, ‘psalms, hymns, and songs,’ [and] seem to recommend to us the book of David’s Psalms.”
Here is a site to start on these particular passages (includes our Rev. Winzer's article on The Westminster Divines as well):
https://renopres.com/2016/04/04/eph-519-col-316-and-westminsters-view/
