<Snipped quote by Kho>
The way I figured it, If you just swear by Amul, you're fairly serious but could be lying. Nothing to enforce you either way.
If you do what Vestec has been doing and putting might into it, you're making a binding contract that forces both sides to uphold their bargain or face serious consequences. Whether those consequences include Amul himself, that is up in the air.
It's a bit like how in the Immortals After Dark series by Kresley Cole, if you swear to the Lore you are
bound to keep that oath or face terrible consequences, and depedning on what you swore to do, it could result in your death. Whereas if you just vow to do something and don't include the words "I vow to the Lore," you are not bound to that oath except for your own word, and we all know that promises are made and broken all the time.