Chrysostom says that the difference between psalms and hymns are that the psalms are the OT psalms and the hymns are the songs sung by the cherubim, as seen in the prophetic literature.

https://www.newadvent.org/fathers/230309.htm

Calvin says that "psalms" are songs sung to instruments, "hymns" are songs of praise, and "spiritual songs" are songs with praise and exhortations about other matters.

https://ccel.org/ccel/calvin/calcom42/calcom42.v.iv.iv.html

Many Puritans argue that "psalms, hymns, and spiritual songs" are three classifications of the psalter, and thus Col. 3:16 and Phil. 5:19 tell us only to sing the psalms.

Some contemporary commentators argue that the classification refers to OT psalms, NT canticles (like the Song of Mary or Song of Simeon), and charismatic/prophetic song (which would be truly new, on the part of the singer).

Many commentators simply say that "psalms, hymns, and spiritual songs" are three ways of saying basically the same thing-- Sing pious religious songs.

Basically-- there's no consensus. Not over the course of history and not among current biblical scholars.

One more-- Gregory of Nyssa says that "psalm" means a song sung to music, "hymn" means a cappella, and "spiritual song" is a general term including both.

http://classic.net.bible.org/dictionary.php?word=Hymn