I think you must be listening to the first two bars of the "Melody C" of both Good Egg and Gusty Garden and, because these two particular bars have the same rhythm, you're generalizing that the entire songs are basically rearrangements of each other.
It's only true if you consider basically any two pieces of diatonic thematic music as being essential rearrangements of each other, whether notes, or chords, or instruments. That's the fundamental nature of music. By this definition, any two rock songs are rearrangements of each other. Any two folk songs are. Of course there are similarities between two orchestral Mario tunes. I demonstrated that above.
But apart from two bars of similar rhythm, your specific example of equivalence is musically unfair.