The vernacular names in English (UK/US etc.) are little standardised (compared to the Nordic system in which official names and spellings are provided). Marigold thus is used also for other species.
To illustrate the confusion by non-standardised vernacular names, the following excerpt from en.wikipedia.org/wiki/caltha_palustris is presented;
"In the UK, Caltha palustris is known by a variety of vernacular names, varying by geographical region. These include in addition to the most common two, marsh marigold and kingcup, also brave bassinets, crazy Beth, horse blob, May blob, mare blob, boots, water boots, meadow-bright, bullflower, meadow buttercup, water buttercup, soldier's buttons, meadow cowslip, water cowslip, publican's cloak, crowfoot, water dragon, drunkards, water goggles, meadow gowan, water gowan, yellow gowan, goldes, golds, goldings, gools, cow lily, marybuds, and publicans-and-sinners.[5] The common name "marigold" refers to its use in medieval churches at Easter as a tribute to the Virgin Mary, as in "Mary gold". In North America Caltha palustris is sometimes known as cowslip. However, cowslip more often refers to Primula veris, the original plant to go by that name."
I rather prefer Caltha palustris.