Answered by Ustadh Tabraze Azam
Question: I understand that something is only an oath if you use the words ‘by Allah’ or ‘I swear by Allah’ or something similar. However I’m still not clear on what distinguishes an oath from a promise. For instance, if you are talking to Allah and as you are talking you say ‘I promise Allah I will do such and such’, or ‘I promise to Allah i will do such and such’ or indeed ‘I promise by Allah I will do such and such’ are these considered oaths or promises?
Answer: Assalamu alaikum wa rahmatullahi wa barakatuh,
I pray this finds you in the best of health and faith, insha’Allah.
The ruling of using the phrase “I promise to Allah” would be considered according to the custom (`urf) of a particular place. Thus, if it is used for oaths (yamin), it would be considered as such. If not, it would be considered a promise (wa`d).
Likewise, if one intended an oath (yamin) by using such a phrase, it would be considered as such. However, if one did not have any intention, intended a promise, or cannot remember, it would not be considered an oath (yamin).
In any case, it is important to note that what is considered is a verbal utterance of the phrase. An internal  promise (wa`d),  vow (nadhr) or,  oath (yamin) is of no legal implication.
[Nahlawi, al-Durar al-Mubaha; Haskafi/Ibn `Abidin, al-Durr al-Mukhtar/Radd al-Muhtar]
And Allah knows best and He alone gives success.
Checked & Approved by Faraz Rabbani