Bobby Gilles explains the differences:
In Sing With Understanding: An Introduction to Christian Hymnody, Harry Eskew and Hugh T. McElrath describe a hymn as a kind of poem set to music. They further write, “It should be simple and metrical in form, genuinely emotional, poetic and literary in style, spiritual in quality, and in its ideas so direct and so immediately apparent as to unify a congregation while singing it.”
Most song lyrics are not really meant to be taken as poetry. If you read them aloud without the music, the lyrics might not seem as powerful. They were meant to be taken with music, and were likely written after or at the same time the music was composed.
Hymns are likewise meant for singing, of course, but hymn lyrics are typically crafted as poetry, independent of music (at least, this is true of the hymns of our past by hymnists like Wesley, Watts, Cowper and Newton). When you read a well-crafted hymn such as “When I Survey The Wond’rous Cross,” you will feel the cadence, even if unaware of the melody composed for it. This is why composers can keep writing new tunes for old hymn texts. It’s also why many people (particularly in ages past) would read hymnals as they would any devotional book, and even delight in the hymns they’d never heard.
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