First of all, its "career". Where I come from, "carrier" is a common mispronunciation and spelling this word that way is often a result of this error, so do confirm you are saying "cuh ree ar" and not "carrier". Back to your question: a career is long term and a job is short term, and may or may not be related to your career. Eg: You can have a career as a teacher (I.e. your chosen profession), and for that you worked first in School A (your first job), then School B (your second job) and so on. Then let's say you needed to take up work in a supermarket because your teaching job isnt paying enough, but you dont want to switch your field, so that would be a job too but not a career. Jobs can be full-time, part-time, or freelance. A career is not.

Taking up a career? I would say “choosing a career.” It sounds more serious and long-term. “Getting a job” could mean a part-time job, full-time job, or a gig. It’s more general.

Getting a job means that you work and someone will pay you. I am not familiar with the other expression. Not something I would expect from a native American English speaker.