AppleTV+ Subscription Mystery

Dear Mr J Burger, thanks for taking the time to reply. Your answer's so clear and succinct and I feel like I should be able to easily understand it but I'm still not getting it. I'm not a tech-head, but I can usually work through these issues - except not this time - so I must be misunderstanding something obvious. Let's see:

• Prior to subscribing (via iPhone, to view shows via Amazon Firestick - firstly on older Samsung, now on new lg tv - in case that's relevant), I was already able to watch Ted Lasso, Dead Horses (or Slow Horses?), Loot, Coda and more for free, without a subscription.
• After subscribing (which was around early 2022), I can obviously still view the above, but seem to have quite limited access to other content on AppleTV+ and am repeatedly advised to subcribe.
• I thought with the sub, I'd be able to view most AppleTV+ shows, if not all.
• Could there be some break or incompatibility due to all the different 'bits of technology' (technical term), involved in what I'm eventually able to eyeball - or not eyeball - that is the question.

Dear Urquhart1244, thanks for taking the time to reply and especially for sending the detailed Wiki lists plus the details on subscribing and on the Apple TV App Channels.

Unfortunately, even with all that excellent info and knowing it should be easy to grasp, I'm still a bit stumped as to how the subscription works within this multi-layered beast (no offence to Apple). Perhaps I'm over-thinking it, but the horrible reality is that I'm no spring chicken these days and this shows me how digitally illiterate I've become.

Hate that - must get up to speed!

Thanks again for replying.