There is a clear distinction based on the Prophet's words: 'Whoever is overcome by vomiting is not required to make up the fast, but whoever vomits deliberately must make it up.' So if vomiting occurs involuntarily against your will, your fast remains valid and no make-up is required. But if you deliberately induce vomiting, your fast is broken and you must make up that day. If any of the vomit is swallowed back down intentionally after reaching the mouth, that also breaks the fast.
Evidence — the daleel
On deen2u
Informational, not a personal fatwa. Consult a qualified scholar for rulings on your situation.