Qual è la differenza tra dank u (wel) e bedankt ?Sentiti libero di rispondere con un esempio.

I feel the difference is similar to 'thank you' and 'thanks' in English. Which means there is not much difference. :-)

Here are all forms I could think of that express 'thank you', ordered by politeness and formality, starting from most polite and most formal:
1) Dankuwel / Dank u wel
2) Dank u
3) Dankjewel / Dank je wel
4) Dank je
5) Bedankt
6) Dank

I think 1-4 match 'thank you' and 5 & 6 match 'thanks'.

In 1 & 2 you are addressing a person with 'u', which is very polite but also a bit formal and distant. I use these towards strangers except when they are younger, when the setting is informal, or when they are colleagues or neighbours. So I use this to staff in shops (unless they are clearly younger than me) or to staff of a company or doctor's office where I am a customer.

In 3 & 4 you are addressing a person with 'jij/je', so while it is still polite, it is more informal and implies equality or familiarity.

I see 5 as the equivalent of the English 'thanks', it's short and polite enough, and not too formal. Perfect for the quick 'thank you' for things that are not too big a deal (a colleague has answered your question, a friend says happy birthday).

I never use 6, as I feel it's too short.

If I feel a big thank you is in order (somebody really helped me out), I will say 'Heel erg bedankt' or 'Ontzettend bedankt'.

If I want to say 'Thank you for ....' I use 'Bedankt voor....'. E.g. 'Bedankt voor je hulp' (Thanks for your help).