We’ll take the nouns first. We can approach these from two directions. First, what did these nouns mean in the Greek language of the first century? Second, how were these nouns used in the Greek translation of the Old Testament (the so-called Septuagint, or LXX)? I think the second question is the key one. Christians in the churches in Ephesus and Colossae, whether from Jewish or gentile backgrounds, would be — or rapidly become — familiar with the Old Testament in Greek, and this would have significantly shaped their understanding of how to use language to express theological ideas. So I used my Bible software (Accordance) to search the Greek Old Testament that was used by Christians in the ancient world.
The Greek word psalmos (psalm) comes about 80 times in the canonical books of the LXX Old Testament. Sixty-five of these are in headings to biblical psalms, two refer to David the psalm-singer, five occur in the main text of psalms, two in Job to refer to a musical instrument, one in Lamentations, and three in the prophets. When Paul says “psalm” you would indeed most naturally think of biblical psalms.
But what about “hymns”? This word (hymnos) only comes 14 times in these LXX books. Half of these refer to psalms in the book of Psalms, and six of the other seven occur in the main text of psalms or in historical books referring to the institution of psalmody by David. Probably when Paul says “hymns” a first-century hearer in Ephesus or Colossae would think also of biblical psalms.
And how about “songs”? The Greek word is ōdē (from which we derive our word “ode”). This comes almost 90 times in the books we are considering. More than a third of these translate a word in the heading of a biblical psalm. Most of the others are used in connection with, or as part of, biblical psalms and temple worship. So, again, when Paul says “songs”, his hearers would most naturally think of biblical psalms.
We can’t be sure that they thought only of biblical psalms, but that would be the most natural and primary association of the words. It is as if Paul is saying, “sing lots of psalms and then more psalms and then some more psalms (and perhaps some other songs)”. This puts a different complexion on these verses and has changed my mind about something important that we ought to be doing in our churches.