GA : « A period of interaction between a visitor's browser and a particular website, ending when the browser is closed or shut down, or when the user has been inactive on that site for a specified period of time. »
Omniture : «A visit is a term that refers to a visitor's access to a website. The visit begins when a person first views a page on your company's website. It will continue until that person stops all activity on the site for 30 minutes. For example, if you log in to www.omniture.com, you have one instance of a visit that will last until you have incurred 30 minutes of inactivity, i.e. you have closed the browser or left your computer. If you are inactive for more than 30 minutes, and then you log on again, it is considered a new visit. SiteCatalyst also terminates a visit after 12 hours of continuous activity.»
In the following scenario: a user views a page then closes his browser for ONE minute before reopening and returning to that same page.
Is this the correct interpretation ?
According to those listed definitions, that is correct.
However in my experience of using both tools, GA counts it the same way as Omniture : that is, if you close your browser, reopen it and hit the page again, it still counts it as the same visit, as long as the ping to their server was made before the 30m timeout.
But to clarify, yes, "visits" are persisted by requests to the tool's server (the image request from the noscript tag or js generated image requests, or via an API).
And another thing to note is that if you delete the cookie(s) set by the tool, it will count you as a new visit (and visitor, though possibly not unique visitor, depending on the tool)