Most of the differences described in the answers so far are imagined rather than real. Many language learners find it hard to believe that 'son' and 'sun' are pronounced the same, but native speakers are accustomed to this.
But most people probably haven't thought before about the difference between career and Korea, and will find it shocking that their job is the same as an exotic place. It is possible to pronounce them differently, but it is not natural to do so.
The only real difference is one that Sara mentioned: in some English accents - e.g. in the US or Ireland, the final 'r' in 'career' is pronounced. I think you can hear this on YouTube rather than having to learn about the IPA and rhoticity.