"Despite the phonetic similarity, to me, this does not sound relevant."

Rhymes in this general sense are classified according to the degree and manner of the phonetic similarity:

Mere phonetic similarity, as between English day and Latin dies (both with the same meaning), has no probative value.

It is not phonetic similarity which matters when utilizing the comparative method, but regular sound correspondences.

The dish is spelled in innumerable ways, all with phonetic similarities.

Finally the daughter, Mary as Myrrha,Lee notes the phonetic similarity of the names.

He determined that there was no phonetic similarity between them.

Nonsense words can be classified depending on their orthographic and phonetic similarity with (meaningful) words.

Was there a phonetic similarity in the Ro- manan language?

This approach is based on the idea that letters that share a phonetic similarity, have similar meaning.