The ideal way of expressing "to try" in Korean is saying "해 보다."
시도하다 - to attempt
노력하다 - to try really hard, to show a lot of effort
하려고 하다 - "was going to do" or "want to try to do"
These would be the main differences, and similar to English, it just depends on the severity of the situation and what you are actually trying to do. They are interchangeable but just depends on the context.
i.e.
- I tried to open this jar of pickles.
- There was a valid attempt made by the athletes.
- Stephanie put in a lot of effort into her science project.
- I want to try snowboarding.