What is the difference between those two words? Are they interchangeable?
Could you please provide some examples of their usage?
Here is from my perception:
antun (more precisely jemandem etwas antun)
However, I cannot think of a scenario where they would be directly interchangeable.
'Tun' is a nowadays rather uncommon word for 'To do' (notice the similarity?), sometimes also 'to put'; in some cases it has been replaced by "machen", but is still used a lot in following cases: 1. merged with other verbs as copula (antun, leidtun...) 2. when someone executes an aforementioned action, especially if there is an adverb as 'modifier' of that action, e.g. ('er tut es gern', 'er tut es oft', 'er tut es freiwillig') 3. Some phrases have it. Like: 'man tut, was man kann' or 'es mit etwas zu tun haben'.
Actually, it has many meanings, just like the English verb 'to do'.
'Antun', however, has very little uses that i know of. It can be used when the action is directed at someone or something. It can be a good or a bad action, but it is more commonly used with the latter. 'Das tut mir nichts an!' ('This (action) does not affect me/harm me') 'Er hat mir böses angetan!' ('He did bad things to me!')
I want to add one thing that is not mentioned in the other answer.
As @Matthaeus is indicating, antun can also be used in a positive way. This usually happens in the following idioms:
This means that you're really excited by something or someone.