[fabricexpert]

It's not because you are a non-native speaker. It's not a widely used English term without the word Insurance in front of it, however it is a standard American English term.

It is also not the costs "not covered by health insurance", rather the insurance premium is the cost of the policy itself.

[dandare]

Interesting, thanks! But from what I know people in US often end up paying extra cash (on top of their health insurance) for procedures, checkups, and drugs. This is rather rare in EU. That should be included in whatever international comparison.