Translator or interpreter?

The difference between a translator and an interpreter is that a translator produces a written document in another language and an interpreter produces spoken word in another language. A translator will usually translate from one written document – be it a Word document, a pdf, a PowerPoint document or even an image with text in it –into another, whereas an interpreter will usually listen to what is being said live and repeat it in another language in real time. However, a translator can also produce a written document based on recorded spoken words.
Basically, if you want to end up with written document in another language, you need a translator, but if you want someone to repeat what’s being said in one language in another language, you need an interpreter.
Should they be a native speaker?