1，我想知道他是不是医生。 2，不管他是不是医生我都想知道（真相，或他是干什么的）

The presupposition differs: 1) you are looking for a doctor or you want to know if 'he' by any chance is one. It presupposes that you have no information of his profession 2) You heard he is a doctor and/or someone told you he is not. So there is a conflict of information. There is a stronger sense of insecurity.

Both sentences are the exact same in my opinion.