They are the same, but in a different language. Jhana is Pāli, Dhyana is Sanskrit. Pāli ist the language of the oldest collection of discourses of the Buddha, on which Theravada buddhism is based. Sanskrit appeared later and is often used in Mahayana traditions.

As far as I know both Pāli and Sanskrit are artificially created languages, by merging various Indian dialects of the time, for the purpose of communicating spiritual/religious teachings across ethnic boundaries.