The English are using an older meaning of the word, "pudding." A pudding is a steamed dish with contents that swell during heating, not the chocolatey glop that we eat.
From the Online Etymological Dictionary:
c.1305, "a kind of sausage: the stomach or one of the entrails of a pig, sheep, etc., stuffed with minced meat, suet, seasoning, boiled and kept till needed," perhaps from a W.Gmc. stem *pud- "to swell" (cf. O.E. puduc "a wen," Westphalian dial. puddek "lump, pudding," Low Ger. pudde-wurst "black pudding," Eng. dial. pod "belly," also cf. pudgy). Other possibility is that it is from O.Fr. boudin "sausage," from V.L. *botellinus, from L. botellus "sausage" (change of Fr. b- to Eng. p- presents difficulties, but cf. purse). The modern sense had emerged by 1670, from extension to other foods boiled or steamed in a bag or sack. Ger. pudding, Fr. pouding, Swed. pudding, Ir. putog are from Eng. Puddinghead "amiable stupid person" is attested from 1851.