No Kat, a plimsoll is the same over here - that rubber soled gym shoe. Can't remember why, but there is also the Plimsoll line on a ship which is it's loading levels - named after someone called Plimsoll who worked out all the mathematics of it - maybe a connection? We also call them sandshoes (abbreviated to sannies or saunies) in Scotland.
I've heard heeled shoes called pumps too - but in the UK they're more typically called court shoes. Pumps to me suggests flat shoes. Three inches?? ALL my court shoes are over three inches! It's when they get over five....!! What about flip-flops do you have them over there? Those flat rubbery beach shoes which are held on by a thong between your big toe and the rest? And just to add to the confusion bedroom slippers are sometimes called baffies here - or maybe thats just my family... Shoeless Mo from soggy Glasgow.