Not quite but I can see why people think so. Both words stem from the same Kanji pair: 切腹. Cut stomach.

But one is read natively (harakiri) with an informal and colloquial feel to it and the other uses borrowed Chinese pronunciations (seppuku) that makes it sound more formal/ritualistic and so it’s used in official documents. But they mean the same thing.

Another related example is Japan’s own name: 日本. It’s usually read as “nihon” but has a special, formal reading of “nippon”.