It is true that browsers do much more computation than "dumb" terminals, but there are still non-trivial parallels. Terminals do contain a processor and memory in order to handle settings menus, handle keyboard input and convert incoming sequences into a character array that is then displayed on the screen. A terminal is mostly useless without something attached to the other side, but not _completely_ useless. You can browse the menus, enable local echo, and use device as something like a scratchpad. I once drew up a schematic as ascii art this way. The contents are ephemeral and you have to take a photo of the screen or something in order to retain the data.

Web browsers aren't quite that useless with no internet connection, some sites do offer offline capabilities (for example gmail). but even then, the vast majority of offline experiences exist to tide the user over until network can be re-established, instead of truly offering something useful to do locally. Probably the only mainstream counter-examples would be games.