Praktikum is a bit more like work experience -- I'd say usually between two and four weeks, probably unpaid. By children in the last years of school to get a flavour of different jobs or just of work life in general, or for a student to try out a job they might like to take after they finish.
Ausbildung takes longer, between two and three years, and trains you for a particular job. You get paid during your Ausbildung and it's a mixture of school and work (it could be several weeks of school at once, then several weeks of work, or the school could be one to three days a week with the remaining days being work). I'm not sure whether that's a Thing in the English-speaking world and thus whether there's a proper name for it.
"Apprenticeship" is one word I've heard to translate Ausbildung, but I think apprenticeship is used more commonly in hands-on labour such as woodworking or plumbing, which in German usually have a Lehre rather than an Ausbildung. But the idea is similar.
This should definitely also be translated as "the practical". I study at a German university and what we refer to within the faculty as "ein Praktikum" is a practical exercise task, for example in the lab or in the field, which at my Australian university were referred to as "practicals".
In US English, I've heard the first year of training for a newly-graduated doctor being referred to as an internship. Other fields of study may have their first year of practical experience being referred to as an internship. Perhaps Praktikum refers to the same thing in Germany?