Difference between "advantages of a car lease" and "car lease advantages"

It is hard for foreigners to understand the meaning of different English sentence constructions.

Do the phrases below mean the same?

advantages of a car lease

car lease advantages

When do we use one or the other?

They mean exactly the same. Their difference lies in terms of style. 'Car lease advantages' is shorter, the alternative follows the construction of languages older than English. You can use both without fear of having said something wrong.

They mean the same thing, but the first is more often used. Here are examples:

The advantages of a car lease is [sic] that the Lessee has no obligation other than to turn in the car when the lease has expired.

For business owners, one of the most important car lease advantages would be that you will be able to deduct some of the mileage that you made for business purposes.

Google gets over a million hits for "advantages of a car lease", and only 22700 for "car lease advantages"; most of the latter are headlines or titles.

You can use either without being misunderstood.

The two phrases mean the same thing but the first would usually be considered better style. Noun stacking, as in the second example, can make sentences difficult to understand:-

...a steroid-induced GABA channel burst duration prolongation...

or sound ugly:-

Your staffing-level authorization reassessment plan...

although it is often used, as drɱ65 δ observes, in headlines where brevity is required.

See here for more examples.