These words are used by Paul in Ephesians 5:19 and Colossians 3:16 to designate the kinds of songs God wants us to sing in our worship. These three terms are very similar in meaning, and can overlap somewhat, but they are mentioned separately. What exactly are psalms, hymns and spiritual songs?
Psalms: While the Psalms from the Old Testament can be and are sung in worship today, it is believed by some scholars that this phrase was not limited to the Psalms from the Old Testament. A psalm is, by definition, a sacred song or poem. It is a song which offers praise and adoration to God for His various attributes and blessings.
Hymns: Like a psalm, a hymn is a song of praise and honor unto God. One possible distinction that some have suggested between a psalm and a hymn is that psalms were inspired songs of praise, while hymns were uninspired.
Spiritual Songs: These would be songs which are based upon spiritual themes, as opposed to songs based upon secular themes. Unlike psalms and hymns, which offer praise unto God, spiritual songs are designed to instruct us regarding the doctrine of Christ or to encourage us to greater faithfulness.
William Hendriksen, in his commentary on Colossians 3:16, has this to say regarding the differences in the terms: "All in all, then, it would seem that when here in Col. 3:16 the apostle uses these three terms, apparently distinguishing them at least to some extent, the term psalms has reference, at least mainly, to the Old Testament Psalter; hymns mainly to New Testament songs of praise to God or to Christ; and spiritual songs mainly to any other sacred songs dwelling on themes other than direct praise to God or to Christ" (p. 162).
Kept in the context of the verses in which they are found, we know psalms, hymns and spiritual songs are to be offered to God from the heart. Also, in singing them we are teaching and admonishing one another.