First of all, I'm and Ex Brit. Born and raised in the UK for 30 years, been here in the USA since 1979 and a US citizen since1992. So I can probably shed some accurate light on this subject.
First, ref. yards and gardens: Oliver is on the right track. Mike 121 has the best short description.
A US yard (apart from being 3 feet

) is indeed the area around your house that is part of the property and is not necessarily fenced in. Back yard and front yard (occasionally also side yard) are subsets of that. (BTW: Jamaicans use a similar term "me yaad" which includes the entire dwelling.) It is not necessarily developed or landscaped but typically is, at least partially depending on exactly where you live. (In some places, local city or county codes actually require front yards to be landscaped. Not to be confused with HOA's - home owners' associations - probaby better describes a A-H's... if you get my drift.) If you have a large property which includes acreage such as pasture, woodland, etc., that is typically not included in the description of yard. Think of it this way, the yard is the entire immediate general purpose around your house and the garden (if it exists) is the smaller area of the yard set aside for specifically cultivating stuff.
To be technically correct, before anyone nit-picks, your yard does not include areas that may be technically owned by you, but are in fact part of the public street, sidewalks, etc. That situation exists in many cities - it's yours, but it's not really yours - and usually the city is responsible for upkeep, modifications, liabilies, etc. I think they do it to avoid the complextiy of having to have titles (deeds in the UK) to lots of odd shaped pieces of land.
In the UK they would typically refer to the whole yard thing as their garden.
For commercial use, a yard is a yard wherever you are.
However, just to confuse you again, a place where you can go and visit to enjoy the plants etc. publically, is usualy referred to as a garden in the US as well, but that includes the entire propery, parking lot as well. For example the Japanese Gardens and Rose Gardens in Portland OR.
In the US, a garden is an area of the yard that is cultivated for some specific purpose. Usually this is for vegetables, herbs, or fruit, etc., but some times for flowers and such. Often there is no discernable physical boundary. We have 4 raised beds and several half barrels that are our garden. The rest of our yards - front back and sides - have lawns and borders with flowering plants, shrubs, trees, etc. - and a few fruit bushes and herbs mixed in but they are not "garden". The motorhome parking pad and garage driveways are also part of the yard.
OK... I just opened another can of worms... For you Brits, our motorhome is not a "camper van" - by any stretch of the imagination. It's a class A diesel pusher (rear engine) RV, the size of a decent bus - 37ft long x 9.5ft wide and going on 14 feet tall including the AC/heat-pumps, satelite dishes and various other stuff on the roof and it's by no means one of the longest class A RV's. They go typically from 30ft to 45ft. I'll get to trailers and caravans and othe RV's another time...
Compost:
Compost or composting mean the same thing on both sides of the pond, as does potting soil. (The latter may include some of the former.)
Gas:
Gas is gas in both places - except when it's not.
What the Brits call petrol, we call gasoline, which is more often than not shortened to just gas. However, in formal instructions, manuals, etc., or anywhere else necessary, is typically written in long form as gasoline - for obvious legal liability reasons. So gas is really a "slang" term and it's meaning is understood by context.
But LP gas (LPG), natural gas, and and other types of gaseous substances are referred as gases in the US as well.
BTW: we don't use Calor gas, which is or was a proprietary blend of Propane and Butane, for general purposes. In fact, we don't typically use Butane that much except in tiny 1lb cylinders for very compact portable use. We use propane - also for bulk heating for homes and other purposes, where permanent bulk storage tanks are mostly used and refilled on site by local companies. Natuaral gas is also used, but piped in like it is in the UK.
Wrenches:
Yes, a wench in the US is a spanner in the UK. It is usually either open ended (occasionally called a c-wrench) or box ended (ring wrench if my memory serves me correctly?), or a combination wrench with one of each at ether end. Just to confuse that simple definition, a box wrench (as oposed to box ended) is also a tube wench - I believe in both places - and is a short steel tube with the ends formed into hexagons and used with a cross bar inserted through holes. Incidentally, we in the USA have adjustable pipe wrenches which I believe are still called monkey wrenches in the UK.
I'll quit there... for now. I'll come back with some of the more amusing fun alternate names for things later.