A "Praktikant" is somebody who does a 'Praktikum' which is an internship. You are working for a rather short period of time practically at a company for instance, just to see what exactly they do, so you can get an idea about that particular occupation. You usually do it for free, for your own education or because it looks good on an application, without them paying you for your work. Likewise, you don't have any 'rights' or anything like that, they can basically kick you out anytime they want. "Azubi" is a shortened colloquial version of "Auszubildender", that's somebody who does an "Ausbildung" i.e. apprenticeship. That is usually paid work that you do for a few years, you thoroughly get educated in that job, you have rights, they cannot simply 'fire' you, after you're done you can either work at that company as a full employee if they liked your work or you can go to some different place and work there.