Many of these tunes and texts were in effect written "by committee." In other words, the ideas have been sung and modified and developed over many years from many situations. Verses have been added and arrangements have been made that may or may not have modified the original melodies. The originals may never have been written down, so how would we know? What we have had handed down to us is the best of the collective memories. Each succeeding generation has had an arranger or two that puts his unique stamp on the piece and gives it new life.

The song leader or clergyman would stand up and announce the page of text and state which tune it would be sung to. Some hymnbook collections today have a list of tunes and texts in the glossary that gives meters and suggestions for matching tunes and texts. Only in recent times have the hymn texts and tunes become so synonymous. Then again, there are also newer hymns that were written with composer and lyricist collaboration and would never be considered for alternate tunes. (But very likely could be!)
For example, "Choose the Right" was written by a separate author and composer, Joseph Townsend (1849-1942) and Henry A. Tucket (1952-1918) sometime before 1909. Since the leaders of the Church made "Choose the Right" such a motto for the youth and even created the CTR shield logo and rings, no one even thinks of putting those words to a different melody. However, there have been many new arrangements made. Here's mine:
"Choose the Right" - sung by the Fruit Heights Stake Children's Chorus and a Young Women's Chorus