In this wiki: https://ja.wiktionary.org/wiki/うらめしい, the word "恨めしい" is simply explained as "憎らしい" in one of its items.
Are there any differences?
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You could have used a better dictionary. There are better free online ones like デジタル大辞泉. But here's what 明鏡国語辞典 says:
One meaning of 恨めしい is like "vengeful". It's a strong word used after someone has been badly affected by someone. Stereotypical Japanese ghosts (幽霊) use this word often. See also: Translation of うらめしや
憎らしい is like "odious" or "hateful", and is used in a wider variety of situations. Basically it's an antonym of "lovable". You can safely say 憎らしい笑い方だ when you saw someone for the first time on TV. You can jokingly praise someone like 憎らしいほどに強い "He's so strong I almost hate him".