These discussions suggest that though oath, vow, and pledge are all promises, they have different focuses. An oath is a swearing in the presence of God with regard to a commitment one is making to one or more other people (as to tell the truth as a witness in court, or to uphold the dignity of one's office).

As nouns the difference between oath and swear

 is that oath is a solemn pledge or promise to a god, king, or another person, to attest to the truth of a statement or contract while swear is a swearword. 
 

As verbs the difference between oath and swear

 is that oath is (archaic) to pledge while swear is (transitive) to take an oath or swear can be to be lazy; rest for a short while during working hours. 

 

As a adjective swear is

 heavy.

 

Oath vs Affirmation 

One swears by god a number of times in his life in front of family and friends to prove a point about himself or someone else. But the same swear by the name of God is called as oath in a court of law. Oath though having no legal force is meant to be persuasive as there is the force of religion behind it. When a witness is called in a court of law to give his statement, he is asked to take an oath in the name of his religion before he speaks. This is done to invoke fear of a higher authority (God Almighty) if he falsifies or does not speak truth. Affirmation is another way of making a promise to abide by rules and to perform duties faithfully. What then is the difference between an oath and an affirmation? Let us take a closer look.

Oath

All higher public offices have this oath taking ceremony to induct new members and even the President of the US has to swear in the name of God to fulfill all the duties assigned to him in good faith and to the best of his abilities. An oath can be oral or written or both depending upon the public office in question and the person who is taking oath may have to append his signature on the written oath. As the person talking oath swears by the name of God, he actually invites punishment from this higher authority should he break the promise while performing his duties.

Affirmation

An affirmation is also a promise that a person makes but without any reference to God. This is a promise that some people use as they are not comfortable swearing in the name of God or do not have a faith or religion. An affirmation is just like an declaration that a person makes in words and in front of many people.

An example of oath– I do swear