The most common case is that the aircraft sold to non CATOBAR navies/air forces is built to a different configuration.
For example, the Canadian, Spanish, and Swiss F-18's were each sold under a different configuration. Some of the weight penalties, maintenance and upkeep costs, and the substantial training costs to maintain CATOBAR currency and proficiency were not a concern and not needed. This makes sense: since those flying services didn't have a carrier operations requirement, but they liked a variety of features that the Hornet provided (such as two engines).
Reasons for the selection listed by the Canadian Forces were many of
its requested features were included for the U.S. Navy; two engines
for reliability (considered essential for conducting Arctic
sovereignty and over-the-water patrols), an excellent radar set, while
being considerably more affordable than the F-14 and the F-15. The
CF-18 was procured from 1982 to 1988, at a total capital cost of $4
billion in 1982 dollars.
Interestingly, that early Canadian buy retained most of the CV features, and IIRC they were the first non US buyer of the aircraft. (Memory foggy on that one).
Export Hornets are typically similar to U.S. models of a similar
manufacture date. Since none of the customers operate aircraft
carriers, all export models have been sold without the automatic
carrier landing system, and Royal Australian Air Force further removed
the catapult attachment on the nose gear.
For the non CATOBAR case, the current plan to deploy Marine F-35B's on Royal Navy carriers answers the rest of your question.
LONDON — The U.S. Marine Corps will deploy its Lockheed Martin F-35B
Lightning II strike fighters on combat sorties from Britain’s new
Queen Elizabeth-class aircraft carriers, a senior U.K. Royal Navy
officer has confirmed.