Trolley is more likely to be used in the UK, whereas cart might be US. Otherwise they are basically the same thing. Depressurisation is more specific to air pressure, e.g. airplanes, space. Decompression could be used similarly but has other uses too, e.g. file compression.

shopping or baggage "trolley" and cart" in my experience are the same thing. Trolley is more British and cart is more American. For me decompression and depressurisation are the same but there may be a subtle difference for scientists

No US native would use "trolley" unless they were trying to sound British. Here, a trolley is an electric streetcar, of which we have very few these days.