The popular usage of the word "hymn" to refer to a traditional musical style is probably a consequence of the indiscriminate use of phrases like "worship songs" to refer to all contemporary Christian music. Of course hymns are worship songs, and worship songs are hymns, but contradictory meanings are quite common in English.
OPs definition of a hymn as any song giving praise or adoration to a deity is extended by HELPS word studies,, in defining the Greek word humnos, as giving honour, praise or thanks to gods, heroes or conquerors. Yet even the most traditional hymn books contain "hymns" which reflect on some aspect of Christian experience or biblical theology, or make prayers and supplications. Are "Stand Up, Stand Up for Jesus", "Lead kindly light", "Dare to be a Daniel", "Just as I am", "God save the Queen", "The Lord's my shepherd" and "I heard the voice of Jesus say" not proper hymns?
When is a hymn not a hymn? Am I an animal? Is white a colour? Is the night part of the day? Are Protestants Catholic? Is a tomato a vegetable? Does a pound of gold weigh as much as a pound of potatoes? Was the first man mentioned in the Bible Scottish? All these have different answers in different contexts, and it is probably futile to argue that a common usage is just plain wrong, if it has already entered the language.
In the Epistle to the Colossians chapter3, verse 16, and elsewhere, we read of psalms and hymns and spiritual songs. But what is a psalm, what is a hymn and what is a spiritual song?
Matthew Poole said that some would distinguish them by the method of singing, as well as the matter sung. Some commentators interpret a psalm as referring only to ones in the Book of Psalms, The Geneva Study Bible suggests all godly songs are psalms and include hymns (which praise God) and "odes" (the Greek word rendered "songs") as being particularly artful and fuller of music, in particular. Calvin, at one point anyway, supposed a psalm required accompaniment by a musical instrument. while a hymn might or might not. Some, particularly those who believe in Exclusive Psalmody (the idea that only psalms should be sung in church) interpret hymns and spiritual songs as simply subsets of the Biblical psalms. William Kelly supposes (his word ) that a psalm was a more stately composition, but not necessarily from the Bible. The Cambridge Bible Guide suggests the Magnificat and the Nunc Dimittus (both from Luke 1) count as psalms, though others consider them hymns, and others songs. . HELPS Word Studies suggests spiritual songs were impromptu or spontaneous, while some suggest they were sung by individuals or small groups (choirs, worship bands) in contrast to psalms which were sung by the whole congregation.
Whether the Colossians understood the difference is not very important, since they were urged to sing all three anyway. But there is no consensus, now, about what the difference was then.
Attitudes to church music have varied. St Hilary of Poiters wrote many hymns and included in them doctrine opposed to the Arian heresy, Luther and Wesley were great hymnodists, seeing hymns as a great way to impart knowledge and understanding. Preaching and liturgy (in the widest sense) are vital but perhaps hymns more than anything else inculcate the beliefs of a people.
It is said that a hymn is essentially a poem, something that could be read or prayed without music, but is set to music. A hymn is something that is sung in its entirety by the whole congregation. A choir or worship band may lead,. or sing descants or harmonies, but all join in the entire hymn, A hymn consists of stanzas , each with identical rhythm. Yet it is as difficult to define a hymn as a poem. Such hymns as the Te Deum or the Veni Spiritus or the Ave Maria are not metrical, though metrical versions exist. Ultimately a hymn is whatever somebody thinks a hymn is.
There is a story in several places on the web, but to whom it is attributable I do not know:
An old farmer went to the city one weekend and attended the big city church. He came home and his wife asked him how it was.
“Well,” said the farmer. “It was good. They did something different, however. They sang praise choruses instead of hymns.”
“Praise choruses?” asked the wife. “What are those?”
“Oh, they’re okay. They’re sort of like hymns, only different,” said the farmer.
“Well, what’s the difference?” asked the wife.
The farmer said, “Well it’s like this … If I were to say to you, ‘Martha, the cows are in the corn,’ well that would be a hymn. If, on the other hand, I were to say to you, ‘Martha, Martha, Martha, Oh, Martha, MARTHA, MARTHA, the cows, the big cows, the brown cows, the black cows, the white cows, the black and white cows, the COWS, COWS, COWS are in the corn, are in the corn, are in the corn, in the CORN, CORN, CORN, COOOOORRRRRNNNNN,’ then, if I were to repeat the whole thing two or three times, well that would be a praise chorus.”
As luck would have it, the exact same Sunday a young, new Christian from the city church attended the small town church. He came home and his wife asked him how it was.
“Well,” said the young man, “It was good. They did something different, however. They sang hymns instead of regular songs.”
“Hymns?” asked the wife. “What are those?”
“They’re okay. They’re sort of like regular songs, only different,” said the young man.
“Well, what’s the difference?” asked the wife.
The young man said, “Well it’s like this … If I were to say to you, ‘Martha, the cows are in the corn,’ well that would be a regular song. If on the other hand, I were to say to you,
Oh Martha, dear Martha, hear thou my cry
And incline thine ear to the words of my mouth.
Turn thou thy whole wondrous ear by and by
To the righteous, most glorious truth.
For the way of the animals who can explain
There is in their heads no shadow of sense,
Hearkenest they in God’s sun or His rain
Unless from the cool, tempting corn they are fenced.
Yea those cows in glad bovine, rebellious delight,
Have broken their shackles, their warm pens eschewed.
Then goaded by minions of darkness and night
They all my mild Chilliwack sweet corn have chewed.
So look to that bright shining day by and by,
Where all foul corruptions of earth are reborn
Where no vicious animal makes my soul cry
And I no longer see those foul cows in the corn,
then, if I were to do only verses one, three and four, and change keys on the last verse, well that would be a hymn.”