I see the 2 being used interchangeably perhaps way too often.
But to me personnaly, submission is more a state of mind and does not necessarily have anything to do with bdsm practices. A true submissive will defer in business, traffic, walking, etc.
Slavery is both a mental and physical state where the person submits in total to his / her owner.
Slavery is an all encompassing life style, submission is perhaps at times a game played by one for sexual and mental gratification.
My opinions and beliefs only, no harm or benefit in agreeing or disagreeing.