Short answer, no.
Long answer, Here's the opening snippet from sheet music of both. You'll see both the rhythm (lengths of notes) and scale positions (which notes are different.
In the former, based on this sheet music example in D major (2 sharps), the scale positions go 5 5 8 8 8 8 8 8 7 8 9 (assuming we start on the D below middle C, D3).
In the latter, here notated in F major (1 flat), the scale positions go 5 6 8 8 8 8 6 5 3 5 8 (starting on the F below middle C, F3).
As you can see, these are somewhat similar but different.
As for rhythm, this is a little less set in stone, as they can be sung to different rhythms. I've chosen here notations representing what I'd consider the most common versions as sung colloquially. You can see the former is of the pattern dotted-quaver, semiquaver, repeated 4 times (then crotchet at the end, but this is less noticeable).
The latter is sung 'straight', in simple quavers, though sometimes the 'com-ing' is sung as semiquaver, dotted-quaver -- the opposite of the above.
Sophie Parker
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