Is saying: "Heal me, O Allah, so that I may give charity" (a supplication) and "If Allah heals me, I will give charity" (not a supplication) considered a vow? And when is the phrase considered binding?

The phrasing "Heal me so I may give charity" is open to interpretation regarding commitment or lack thereof, and there is no specific scholarly discourse on it. Whereas "If Allah heals me, I will give charity" is considered by many jurists to be a binding vow (nadhr (definition)) due to its obligatory nature and the circumstantial evidence indicating an intention of making a vow. They cite the hadith (definition): "Whoever vows to obey Allah, let him obey Him." Some jurists, however, view it as a promise rather than a vow, unless one intended it to be binding.