That wasn't the demarcation line either: late feature phones (when they were already called that, because smartphones were very much a thing already) had surprisingly capable browsers (and Wi-Fi, and GPS, and external memory). I already became a web community addict on my Sony Elm. The difference was all about user-installable apps beyond what was offered by J2ME, since what already felt like eons ago.
Post-iPhone that demarcation got muddled a bit by touch-driven UI and the occasional touchscreen feature-phone will be considered a basic "smartphone" by many, but in the historical context when that distinction still mattered it was all about the installables, and J2ME did not count.
PS: neighbor poster reminds us that the iPhone at first did not have user installable apps either, I guess that could be seen as muddling my demarcation line even more. But on the other hand the reality was that when it happened, the iPhone was so much a standout that nobody really cared where it would fit in the emerging field of mobile phone classifications, it was just The iPhone. And iirc "smartphone" as a term wasn't quite as established as we like to think it was, the conceptual bound were more clear than the name. When "smartphone" eventually emerged as the definitive shared superclass of iPhones and Android devices it inherited almost accidentally (and there's-an-app-for-that era Apple did not try too hard pointing out that inaccuracy...)