ill-fated means to have bad luck. For example;

Johb had somehow survived his first ill-fated trip and was now returning on a second mission to the same city.

star-crossed has a positive meaning. It is used almost exclusively for the expression "star-crossed lovers" which means two lovers that were brought together by fate.

Kind of like 緣分 for lovers.

But if you read Shakespear's Romeo & Juliet he uses the phrase 'star crossed lovers' to describe their meeting, but they do not meet a good fate in the end.

Thanks so much Benjamin. So "star-crossed lover" means two lover that were brought by fate.

But their fate are good or bad? Do it matter?

Their fate is good.