Here is the sentence:
Las religiones quieren aumentar las virtudes de las personas para que tengan una conducta o un comportamiento positivo.
I just want to know, what is the difference between "conducta" and "comportamiento"?
Conducta refers mainly to human behaviour, while comportamiento is more general. But the difference is mainly of collocation, I think. There are certain contexts where only one of conducta or comportamiento is permitted. For example, you can say
el comportamiento de las variables meteorológicas
but you cannot say (or it would be a bit weird to say)
la conducta de las variables meteorológicas
Similarly, you can study el comportamiento animal ("animal behaviour") but not la conducta animal.
Also, conducta tends to imply good behaviour, or (self-)control, while comportamiento is neutral (but note that the verb comportarse can mean "to behave well", while conducirse cannot be used in this way).
It seems that some theories of psychology have a clear distinction between what they formally call conducta and comportamiento. For example, on a psychologists' forum I found this:
A grandes rasgos conducta y comportamiento son términos muy similares. No obstante, existen ciertas diferencias. La conducta es la parte observable del comportamiento ante un estímulo externo. El comportamiento engloba a la conducta e incluye aspectos conscientes, inconscientes, públicos o privados, voluntarios o involuntarios.
Translating: "Broadly speaking, conducta and comportamiento are very similar terms. However there are some differences. Conducta is the observable part of comportamiento when faced with an external stimulus. Comportamiento includes conducta as well as conscious or unconscious, public or private, voluntary or involuntary aspects."
This seems to reinforce the idea that conducta means "how a human being chooses to behave" while comportamiento means "how something acts or reacts".