FOP and PBA are just different organizations (unions i think). either card works interchangeably. Keep in mind though.... if you give up one of those cards. The cop you give it too might very well reach out for the cop that gave the card to you. so... you better be ok with the cop who gave it to you knowing why you were stopped.
if you refuse the sobriety or breathalyzer tests the cops will charge you with refusal. IN which case they wont have to prove you were drunk just that you were driving. The penalty for refusal is exactly the same as it is for drunk driving. a buddy of mind learned this the hard way in NJ.
You aren't quite correct in your statements above.
The "Fraternal Order of Police" is just that, a fraternal organization. The lodges, which is what a local organization is called, can either be a social organizations made up of LE members, family and other "associate members' from all manner of jurisdictions or they can be open to the membership of only one department. In the latter case they are almost always also collective bargaining units for that membership.
The Police Benevolent Association are a group locals, which is what the local organizations are called, and are always only open to membership from a specific law enforcement department and are always collective bargaining agents for that group.
The FOP does not care if you belong also to the PBA. The PBA very much cares if you also belong to the FOP, having spawned court cases in several states to sue for the right to kick members of the PBA out of the locals [black balling] if it is found they are also members of the FOP.
The first, last, and only time you will see me write this: Unofficially, what you are referencing are called "courtesy cards". I will simply say that they imply the person carrying one is a friend or family member of the officer whose card it is and it is presented from the presenter as a third party request for professional courtesy. It doesn't obligate the officer presented the card in any way and whether that request is honored will be totally at that officer's discretion. Though in truth in minor situations such request is far more often obliged than declined.
Officially such cards are simply ways of indicating the card holder is a friend or family member who supports their friend or relatives FOP or PBA safe driver program. The cards are neither the property of the holder or of the officer who signed it, but belong to the state FOP or PBA organizations [or issuing authority in other cases] and can be taken by any law enforcement officer and held. IOW, if presented to an officer that officer may determine you shouldn't be carrying it and will hold it. Normally it would be forwarded through the state delegate of that organization back to the issuing officer with an explanation of why it was held.
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The refusal to take the breathalyzer exam in NJ [NJSA 39:4-50.2] isn't issued instead of the the Driving while under the influence charge [NJSA 39:4-50], but in addition too. So if you refuse a lawful order to take either a breathalyzer or blood exam you can be found guilty of both refusal of the implied consent law AND driving under the influence.