Difference Between Submission and Obedience

submit (v): 1) to give over or yield to the power or authority of another; 2) to present for the approval, consideration, or decision of another or others: to submit a plan; to submit an application;

obey (v): 1) to comply with or follow the commands, restrictions, wishes, or instructions of; 2) to comply with or follow (a command, restriction, wish, instruction, etc.).

As you can see, by definition, submission is a far greater thing than obedience.

Submission requires love, respect and a willingness to yield to another. Obedience on the other hand doesn't require any personal relationship between the one giving the "command" and the one obeying the command.

For example, a Private in an army might obey his Commanding Officer, but may also hate and disrespect his Commanding Officer by talking negatively behind his back or even plotting to do him evil. The Private's motivation to obey his Commanding Officer may be out of fear and self-protection or self-promotion. Either way, he is obeying only to improve his current situation, which is only self-centered.

But a Private who submits to his Commanding Officer will not only obey, but he will be a blessing to his Commanding Officer. This happens because submission requires a personal relationship, where mutual love and respect are enjoyed.

While a wife may obey her husband, if she does not submit to him, they will have a marriage more like an orderly military company, rather than a loving and gracious relationship with one another. A submissive wife not only brings order to her house, but she excels above a merely obedient wife by blessing her husband with the beauty of Christ—and everything pales in comparison to Christ.
"And the world is passing away along with its desires,
but whoever does the will of God abides forever."
~1 John 2:17, ESV