The lyrics look different. In fact I don't even know why it came up in the Google search with the lines from The Christmas Bells.

One problem is that there are so many Christmas carols referring to bells or with the word in the title.

From the link above to Henry Knight song with sheet music and MIDI file

1. O’er hill and dell
The Christmas bell
Is ringing far and wide;
Let all rejoice,
With cheerful voice,
And peace on earth abide.
For Christ is born
This happy morn,
Hark! Hark! the Angels sing;
Good will and love,
From Heav’n above,
To all mankind they bring.

2. With holy mirth,
To greet His birth,
Draw nigh that Infant’s bed;
Be not afraid,
For He is laid
Within a lowly shed.
There bend the knee,
For this is He,
Of David’s royal line,
Who reigns alone
From manger-throne,
In Majesty Divine.

3. Nowel! Nowel!
Our song shall tell
To people yet unborn,
How Christ the King
Did gladness bring
Upon this happy morn.
The gloom departs
From faithful hearts,
For lo! the Lord is here.
Come one and all,
Before Him fall,
That Blessed Babe revere.