Answer: Yes and No.
Explanation: Fun is when you're having pleasure or amusement in something. Enjoy is taking delight in something. However, it is quite hard to determine a different since if you're having fun, you must be enjoying yourself. And if you're enjoying yourself, you must be having fun.
(I would say they are somewhat synonyms to each other).
Carelessly/ careless / carelessness
True style is the distinctive way a writer uses language
