Which is confusing. Why have a hardware product and a streaming service named identically aside the addition of a non-alphabetically symbol.

When people talk about Apple TV I’m never quite certain which product they’re referring to and have to infer that from the context of their sentence.

Such as "I like my Apple TV" probably implies the hardware box whereas "I like Apple TV" means the streaming service.

Except Apple loves to drop the articles when describing their hardware. E.g. "With iPhone, you can do X, Y, and Z!". So "I like Apple TV" could easily be referring to the hardware box in Applespeak.

but normal people don't, hence this never being an issue

Don't forgot the app! Use the Apple TV app to watch Apple TV+ on your Apple TV!

Isn’t the app just called “TV”? It kind of makes sense if it’s purpose is to show television programs.