I like to think of these three categories of Christian songs in this way:
Psalms are paraphrases of the Psalms set to music:
Psalm 48, Psalm 103, Psalm 72, Psalm 51, Psalm 148, Psalm 32, Psalm 27, Psalm 125, Psalm 9, Psalm 90, and Psalm 1, Psalm 145.
Hymns are, generally speaking, what you find in a hymn book of say 100 years ago:
There's Power in the Blood (Medley), Be Thou My Vision, O Perfect Love, His Name is Wonderful, Great is Thy Faithfulness, Immortal, Invisible, Holy, Holy, Holy, Amazing Grace, The Old Rugged Cross, At The Cross, At The Cross (Medley),My Jesus I Love Thee, Standing on the Promises, Day of Judgment, Day of Wonders, Just As I Am, Crown Him with Many Crowns, The Church is One Foundation, Guide Me O Thou Great Jehovah, I Know Not Why God's Wondrous Grace, Little Drummer Boy, How Deep The Father's Love For Us, Jesus Shall Reign, When I Survey the Wondrous Cross, What A Friend We Have in Jesus, Battle Hymn of the Republic (English) (Korean?) How Great Thou Art, For All the Saints, Silent Night (English), Silent Night (German), Tell Me the Old Old Story, He Arose (sung in English and, I think, Japanese!), The Great Judgment Morning, This Is My Father's World, Joy to the World, I Love to Tell the Story, It Is Well With My Soul, I Must Tell Jesus, Savior Again, To Thy Dear Name We Raise, Like a River Glorious, Tell Me The Story of Jesus, What a Friend We Have in Jesus, I Heard the Voice of Jesus Say, By The Sea of Crystal, He Leadeth Me, Have Thine Own Way, Lord, and Hark the Herald Angels Sing (sung in Lakota, a Native American language), Spirit of God Descend Upon My Heart, O Holy Night (Sung in Navajo, a Native American Language).
And Spiritual songs refer to much of what we call today, Contemporary Christian Music:
Please Search the Book Again, Because He Lives, My God and I, Meeting in the Air, There'll Be Joy in the Morning On That Day, There is Coming a Day, Awesome God, Above All Powers, He's Alive, Mary Did You Know?, Are You Washed in the Blood of The Lamb & I'll Fly Away, They Baptized Jesse Taylor, Plenty of Room in the Family, If That Isn't Love, El Shaddai, He Giveth More Grace, It Is No Secret, This Old House, There is a Redeemer, This World is Not My Home, Lord I Lift Your Name on High, Days of Elijah, And the Gift Goes On, Alabare A Mi Senor (Spanish), Please Don't Send Me to Africa, My God Is Real, I Saw the Light, and Jesus Take the Wheel (See my post Why Jesus Didn't Take the Wheel!).
I don't know what the Apostle Paul would think of the way I categorized Psalms, Hymns and Spiritual songs, but I have a feeling he would say "That's close enough!" I'd like to recommend to you one of the best books I've read on Worship and Christian music:
A Better Way: Rediscovering the Drama of God - Centered Worship, by Dr. Michael Horton
Also recommended reading (my posts)
