I think that you can use both .
Yes, you're right. But it means one thing with 'and' and something else with 'but'.
Both 'and' and 'but' express logical conjunction.
One thing happened, and another thing happened.
One thing happened, but another thing happened.
In both sentences both
things happened. But there is an important difference between the two. 'But' suggests that it wasn't to be supposed that the other thing would happen with knowlegde about the the first thing's occurance. 'But' expresses paradoxes. In a "logical" way, the second sentence could be written this way:
(One thing happened AND another thing happened) AND (IF one thing happened THEN (NOT another thing happened))
This is of course a logical counter-tautology, but this is not a formal language, but a living, natural one.