Even in the UK, there's confusion regarding the term 'compost'. It can mean an anaerobic or aerobic heap in your garden of vegetable peelings and foliage from plants and the like, the end result of that heap, a potting medium, or something created to add to your borders (animal manure compost). The proper way to refer to compost is by putting an adjective in front of it, as in 'potting compost', 'seed and cutting compost', 'garden compost' 'animal manure compost' and so on, which helps to clarify the purposes to which you can put the various forms of compost. Compost is a big subject which I won't go into here.
However, as a Brit, I can make the following observations regarding the different use of language between the UK and the States:
UK Garden: USA yard (yard in the UK means a small, enclosed paved or concreted area)
UK soil: USA dirt
UK potting compost: USA dirt
UK turf or turves: USA sod (sod in the UK is rarely used, but is a non specific term and refers to soil in general, in particular, cloddy, lumpy soil, rarely, turf, but only by much older people)
UK spade: USA shovel (Note 'shovel' is used in UK, but the tool is different from a spade, not intended for digging the ground, but shaped for shovelling things like sand, concrete and the like)
UK plant/seed trays or boxes: USA flats (I think, not fully worked that one out yet, but that's what it seems to be)
UK coriander leaves: USA cilantro (also other parts of the world use that term for the leaves, restricting 'coriander' to the seeds)
Then there's plant names, the one area where there is a really massive difference, the USA tending to use names which are not necessarily commonly used elsewhere, and seeming to prefer 'common' names rather than the Latin or botanical names. For instance, 'Rose of Sharon' - in the UK it means Hypericum, in particular, Hypericum calycinum, but in the States, it seems to mean Hibiscus, though I've never yet seen any American person refer to this plant as Hibiscus, its always 'Rose of Sharon'. Sycamore is another one - in the UK it means Acer psuedoplatanus, but in the States, it refers to Platanus occidentalis, or American sycamore. I'm reliably informed via this site that 'sycamore' in the States may also refer to other types of tree. 'Rose paeony' in the States is actually Paeony, and that's what we call it here, just plain Paeony (or Peony), never 'Rose paeony'. It can be confusing when answering questions, there's a need to establish quite which plant people are talking about, or seeing a photograph.
There's another one I've not quite worked out yet - in the UK, we refer to 'garden centres', meaning usually a large commercial outlet selling plants, pots, various composts, paving and often garden and interior furniture and scented candles and other detritus, or we refer to 'nursery' which means a much smaller commercial outlet which primarily sells plants, most raised by the people at the nursery, and pots. I'm not at all sure what the American terms are for these two different places... though 'Home Depot' seems to refer to an outlet not dissimilar to places like Homebase and B & Q here - they sell plants outside, but inside is mostly DIY stuff.