When someone says "Danke" or "Danke schön", you can can answer with "Bitte schön", "Gerne" or "Gern geschehen". These are common phrases to express a response on thanks. There are several more, and I am sure, also some dialectal variants.

Vielen Dank is a tiny bit more formal then Danke. You can compare it a bit with thanks vs. thank you. But really, it doesn't make a big difference.