They start out similarly, but I think in the first phrase, "Down by the station, early in the morning" - "ning" is on a note lower than the starting note. In "Eensy Weensy Spider", the opening phrase ends on the opening note. Then, in the second phrase, "See the little puffer bellies" is the same range as the first phrase, but in Eensy Weensy Spider, the second phrase ("Down came the rain...") is up a third from the first phrase.