Right. "Realtime" is a bit overloaded of a term, and you've identified the two main interpretations.
The realtime data concept has a bunch of buzz right now and is predicted by some to replace "web 2.0" as the most overused buzzword. The optimistic view of this trend is that always-on internet and smart phones are reaching a critical mass so that there's a demand to know what's happening right now.
In terms of web technologies, the standard implementation for "realtime" updates is to use timers to periodically make AJAX requests. Inefficient, sure, but you can minimize this. Look at sending JSON and using javascript in the browser to add the data to the page as HTML, optimizing database/datastore queries used to serve update requests, and using "lite" versions of your framework if possible (Rails, for example, provides "Rails Metal" for this type of thing).
If you're interested in alternatives to polling, look at ReverseHTTP or comet. Pubsubhubbub looks promising in the web resource space.