Your "career" is the long-term history of the jobs you've had and the ones you will have in the future. When you talk about your "job", it brings to mind the everyday activities you do at work. But when you talk about your "career" it means the choices you make about where to work and how it will affect your future.
To "switch careers" means to change to a totally different kind of work. For example, you can "switch careers" from being a nurse to being a painter.
When you get a different job that's similar to your old job, but with a different company, you say that you "changed (your) job".