In conservative circles which use psalters and hymnals, there is a tendency to use the same tunes to sing different psalms/ hymns. In one church, which I shall not name, the psalms weren't even tagged with any single tune. Rather, based upon the meter, a tune is chosen with the same meter as the verses to be sung, from a selection of tunes matching that meter.
Singing is an activity which engages the emotions, or at least it should. Worship should be from the mind, of the will, and then with emotions arising from the heart caused by the truths sung. We are after all to love God with ALL our heart, soul, mind and strength (Mk. 12:30), and while the intellect and will are primary, yet emotions are not therefore to be neglected. In this light therefore, matching different tunes to different psalms and hymns is actually a better practice. If music is to help us to praise God, then having a fixed tune to a fixed psalm/ hymn would make it easier for us to remember the particular psalm/ hymn/ song, and through this, it would be easier for believers to match them and so remember the psalms /hymns/ songs. After all, shouldn't the goal be for believers to internalize them so they can praise God throughout the week, and not just on Sundays since they can't remember the words and tunes of the psalms/hymns if there aren't holding psalters or hymnals with them?
During the Reformation, the Reformers compose new tunes to go along with their psalters. The new tunes were to facilitate the worship of God. Strangely, some of those in conservative circles cease to compose new tunes, but instead there is a tendency to reuse old tunes for new psalms or hymns. I have even heard of reusing hymn tunes for singing psalms. Historically, even the stricter Reformers who advocated for exclusive psalmody composed, or had someone composed, new tunes for the psalms to be sung in worship. This preference to reuse old tunes is strange, especially since it is not using an old tune which is no more in use, but using a tune for multiple songs.
While there is nothing inherently wrong about using one tune for two different songs, it is much better in my opinion to have one tune to one song. Such will make it easier for believers to own the psalms/hymns/songs as their own, and use it to worship God throughout the week.