These are often used inaccurately as they don’t translate well from other languages.
Let’s use besides to modify the following argument:
I don’t think we should go to the cinema tonight. First of all I don’t like the film. Secondly, there is an unusual amount of traffic in town. Finally, we don’t have any money.
Here we have three supporting claims for not wanting to see the film:
The same argument could be expressed using besides, as follows:
I don’t think we should go to the cinema tonight. Besides not liking the film and the unusual amount of traffic in town, we don’t have any money.
The second sentence (the supports) can be represented:
Besides + claim(s) [nouns] + , + final claim [a sentence].
In this case besides simply means as well as.
Here the meaning is a little different:
I don’t think we should go to the cinema tonight. First of all I don’t like the film. Secondly, there is an unusual amount of traffic in town. And besides, we don’t have any money.
The supporting claim introduced by and besides is much stronger than the preceding supporting claims. In fact, it is so strong that it is really not necessary to consider the previous claims. If we have no money then there’s no way we can go to the cinema!
Again, it’s useful to diagram the structure:
Weak claim(s) + And besides + very strong [and final!] claim
Here the meaning is more than just as well as.
And besides introduces a very powerful claim that makes all other preceding claims redundant.