Yes you answered your own question. Turning iMessage off just forces all messages sent and received to be via sms/mms. And yes, even with it on it discerns idevices vs non-idevices and sends messages accordingly.
The iMessage on/off switch just turns the Apple iOS side of the messaging on/off. iMessage's to other iOS users goes through Apple's servers instead of through Verizon. With iMessage OFF it forces all SMS/MMS text's to be sent through Verizon's network.
I'm sure others can provide a more 'technical' explanation of how the process works. But in short - iMessage ON will communicate to other iOS users through Apple's servers. Keep in mind, NON-iOS (i.e. Android) users will still be communicated to through Verizon's network (for SMS/MMS). So with iMessage turned off - ALL users will be communicated to through Verizon's SMS/MMS.
I am new to the Apple ecosystem and I never really tried the native message app. I am not here by choice I had it thrust on me by my employer. I am at the bottom of the Apple learning curve.
The reason I wanted to use the Verizon app is because messages are available everywhere, on whatever device I choose to use. If I understand how iMessage works (and I may not so correct me if I am wrong) then if I use that my messages will be available on my Apple devices but nowhere else. The Verizon app allows me to view my messages on my MS PC with an app or within the browser. Maybe the Verizon app is not the best choice? WhatsApp? But I digress.......
You are correct - using Apple's iMessage - provided you are signed in with the same Apple ID on your other Apple devices - will allow you to view any/all iMessage threads on all your Apple devices (among do other things like FaceTime, photosharing, iCloud backup's, etc).
You do have a good point with Verizon's Messages+ app and how you can view on any device across all platforms - this is a nice feature for sure.
I unfortunately can't comment on WhatsApp or other apps since I have never really used them and have minimal knowledge about them.
On a positive note, welcome to the Apple world! Hopefully we can help you enjoy your products and answer any questions you have.
I wonder if the reason you don't get some messages is because of the iMessage glitch. See NY tTmes blog on The Flaws of Apple’s iMessage. Perhaps if you deregister? See Apple support article Deregister iMessage: Frequently Asked Questions. As I said I am still trying to figure out how to navigate the Apple world so maybe I am missing the mark here.
No, because the messages which are not showing up are STILL SMS/MMS and not iMessages. In fact, these can even be an occasional message in a thread where I routinely receive and can view messages in Verizon Messages.
For what it is worth, I have iMessage disabled. I prefer using Verizon Messages across platforms as I switch phones quite often. I don't think I have ever had iMessage enabled for this simple fact.
One note to consider about iMessage. While individual messages between iPhones with iMessage enabled will be treated as iMessages, if you send a group message and at least 1 person in the group does not have an iPhone with iMessage enabled, the message will be sent to ALL recipients via SMS/MMS, even iPhones with iMessage enabled.
I recall reading an unofficial way to view iMessages on a PC a while back but I can't remember where I saw it or if it was a lot of hassle. I have very limited experiences with messaging apps but I never stuck with them because I sincerely saw no need for them when native messaging on every device I've used has met my needs. If I'm not mistaken regardless of what method you use you will still receive your messages in the native app also so it's really a question of if you really need to use the additional app on your device or if it would be better to use it in places where you won't/can't access your messages on your device (such as your computer or whatever else you're using to view). That's a personal decision of course but it's something to consider if it's an annoyance to be receiving the messages twice.