What is the distinction between a vow, an oath, and a covenant? How does one know which one was made if one did not make any specific intention or recite any specific formula?
Vow نذر when you commit to do a worship like fasting or praying recommended Prayers like Night prayer, or good act like helping needy or give something in good cause if you get your wish.
Oath يمين is when you take oath to do something good or leave a bad deed like taking oath to leave smoking or leave attending mixed gatherings etc.
Covenant عهد is when you promise Allah (SWT) to do something good or leave something bad.
Fulfillment of vow, oath and covenant is obligatory.
If you don't remember what intention you had, you need to just fulfill what you had committed no matter what was whether vow or oath or covenant as all of them share a commitment which must be fulfilled. Failing to fulfill the commitment is a sinful act.
Wassalam.