Growing up at every family funeral my older cousin (great aunt's kid) would sing this song. It is the only song I can think of that fits the thread, though to honest I don't know what a hymn is and I am too lazy and tired to look it up right now.
Religious music breaks down in multiple categories, some of them overlapping. If you subtract the instrumental composition, then vocal songs are what you have left.
Vocal praise music then falls out into categories depending on how the music is used, from what traditions it comes, and even how it is worded. I'm not versed on religious music outside Western Christianity, so don't apply this outide that.)
There is much music that derives from the Catholic Mass, the formal, structured, sacramental service of worship that evolved in the Holy Roman Catholic Church over centuries, but has been in place for many centuries. It was once only in Latin, so was liturgically in common across the planet, from South America to Europe to the Far East. Musical traditions within the Mass varied from culture to culture, but were initially obviously dominated by the European influences.
The music was focused on choirs and organs and formal music.
Then, the Protestant reformation saw movements that increased the congregation's singing. Germans and Swiss and later others were especially enthused about singing hymns, or songs of praise, in the congregations. Those hymns were sometimes written by famous composers like Brahms, or adapted versions of music great composers wrote for operas, oratorios, or masses, or requiems (masses for the dead, memorials).
But, there were also many hymn writers for both the music and the poems that begain spreading all over. This happened about four or five centuries ago, and was really not unlike our modern explosion of "desktop publishing" as the computer has enabled more people to dissemminate more creations. Four and five centuries ago, it took time for the moveable type printing press to proliferate, but eventually they did, and hymnals became a thing, eventually put in the hands of worshippers in many denominations, written by men and women.
Way back there, carols were also being written. Carols were originally secular music, and associated with dance, but later changes saw them increasingly blur into religious themes, usually more cheerful than hymns, and often less devotional than narrative like ballads. Carols today are included in Christmas services, but are still treated a bit differently than the more classical hymns traditions. It's very difficult to make up a strict set of rules to describe one versus another.
Less formal worship traditions (think megachurches, Pentacostalists, Charismatics, etc.) don't make such distinctions and simply refer to their songs as "praise songs," intentionally stripping away the formal language that makes liturgical music stand apart. And, in that evolution, for many, the modern praise songs do have little distinction from the secular music that exists alongside them. The same is true in reverse.
Amazing Grace is often sung in country and western venues, including bars, with no particular intent to worship at all, merely as a cultural crossover, a song associated with family and tradition.
I was originally a Music Education major in college (after pre-pharmacy) and took a couple of years of music curriculum, before switching to English, so church music is very near to my own interest, and I have participated in diverse denominations from Fundamentalist to Episcopalian.
Hope that helps give a little depth to the question.