Action Dice vs. Character/Monster Dice

I'm just trying to get some clarification here. I understand, per the rulebook, that dice are classified as either character dice (dice that have a character on at least one of the faces) or action dice (dice that don't have a character). By this logic, this would make Sidekick dice in the dice bag/Used Pile/Prep Area (i.e. not in play) character dice because they have a character face on them (and they're obviously not action dice). I also understand, after doing some digging, that character dice (Marvel/DC) = monster dice (YGO). This would lead me to believe that Sidekick dice found in my dice bag to be monster dice. If this line of logic is not correct here, please let me know .
Now, with the card Sangan -- Sacrificial Fiend, its text states "When this monster gets knocked out, you may pull two dice from your bag. If both are monsters, put them in your prep area; otherwise, return them to your hand." I read a ruling on these forums that stated that if I pulled a Sidekick and a non-Sidekick monster die from my bag with this ability, they would both have to be returned to the bag. Why? Are they not both monster dice? This is very confusing.
If I'm missing something here, please explain to me so that I can relay this to some of the other players here in our playgroup.
Now, with the card Sangan -- Sacrificial Fiend, its text states "When this monster gets knocked out, you may pull two dice from your bag. If both are monsters, put them in your prep area; otherwise, return them to your hand." I read a ruling on these forums that stated that if I pulled a Sidekick and a non-Sidekick monster die from my bag with this ability, they would both have to be returned to the bag. Why? Are they not both monster dice? This is very confusing.
If I'm missing something here, please explain to me so that I can relay this to some of the other players here in our playgroup.