Is seborrhoeic and seborrheic the same thing?

Yes, "seborrhoeic" and "seborrheic" refer to the same condition and are used interchangeably, with the former being the British English spelling and the latter the American English spelling. Both terms describe skin conditions related to seborrhea, which involves excessive oiliness and can lead to issues like dandruff or seborrheic dermatitis. The choice between the two spellings generally depends on regional language preferences.