[2023] How Do Conflicting Skill Specifications Work?

Hi all, newb question: I notice with some skill specializations, different branches can have completely different effects that seemingly conflict with each other. For example, I saw a Rogue Marksman skill where one branch turned the base physical damage into cold damage, and another branch turning the base physical damage into fire damage. (Or something along those lines).

If you did a weird spec to try and grab both, would one block the other, or would they do double damage, or the normal damage across two elements?

There was also another scenario for Paladin where you can turn Judgement into an Aura around you, instead of on the ground. But then another spec that turned OFF the ground aspect completely and turned it into more penetration damage. So if you tried unlocking both, would you get an Aura that also penetrates, or would one cancel the other out?

Thanks for the clarification!