Disclaimer: This answer describes Meteor, JavaScript client library for Meteor Server. It was originally added due to ambiguity in the question, and may serve the purpose of clarifying similar ambiguities faced by the visitors searching for similar answers, but unsure about the difference.
To read about Meteor JavaScript framework, please see this answer by xer0x.
As mentioned on the Meteor Server's documentation, Meteor is an implementation of Comet. Comet in turn is a counterpart of AJAX.
In case of AJAX, you usually make a request when the client sees a need to do that. To pull updates from the server, you will need to call the server eg. every 5 seconds.
In case of Comet, the update from the server comes faster, because the connection is persistent. The connection is established by client, as in AJAX, but the server does not respond until it has some update or it reaches execution limit (scripts on the server may have execution limits).
In case of Meteor you just get constant stream of data that needs some specific server-side code (like Meteor Server) and appropriate code on the client (in this case it looks like it is Meteor class).