Work: a paid job that a person is able to do without prior knowledge or experience doing - example: working in a grocery store. Working is necessary in life to be able to provide for yourself and your family. Work is just a way to be able to have an income. Some people that just work and don't have a career are worried about how much money they make and have to budget and balance their money well to be able to provide.
Career: a paid job that a person must have gone to school/college for or had some kind of knowledge/training for it - example: working as a doctor. A career has to be earned such as going to school and earning a degree. For most careers people have a steady income and they don't need to worry because it is just enough money for them to be able to provide for their family without worry.
Vocation: a calling, the reason a person is born - example: I was born to be a psychiatrist. A person lives up to their vocation from the day they are born. If they happen to chose a job that is not their vocation, they may not enjoy their job as much as they would have if they did choose their vocation. Most people have a difficult time trying to figure out what their vocation is throughout life, but once people know what their vocation is, it is obvious and they realize that they could have known it all along.