Hey Nikola, both verbs are actually very close synonyms, the difference is minimal. If you're unsure which to use, "anfangen" is safer in everyday situations, while "starten" is better for machines or official contexts.

There is no difference in meaning, though. We also have the verb "beginnen" which is more commonly used in formal situations or statements. It actually just depends on your personal sense of language and whether you prefer to use one or the other in a sentence.