In the UK we have flats and they are commonly sold on a leasehold basis. Someone or some entity owns the freehold. There are service charges that maintain the skin or structure to help protect the leaseholder's interests. The planning system defines what can be built or operated on a site and building control worries about the construction aspects.
In the USA we have condominiums or condos for short, these feel a bit like UK flats. The title is closer to a commonhold and the HOA is the entity that owns the common areas. An interest in the HOA comes with the condo when you buy so there is no freeholder whose interests are divergent to the owners of the individual units. Zoning is the USA term for what the UK calls planning or urban planning.
Pulling permits and building department inspections are two of the phrases for the 'how something gets built' code.
In both the USA and the UK you will see the term 'apartment' used. The term definitely is used more in the USA. Many people would say that they rent an apartment even if the owner of the unit legally owns a condo. The key issue with the term 'apartment' is it masks a subtle difference in the USA housing market. In America, there are lots of apartment buildings that are not condos and those units will never be condos.