I presume it's direct visits. But looking at the charts for seesmic and tweetdeck, if we assume the cumulative unique visitors to these two services in the past year all downloaded and use the service at least once a month, it adds maybe 5-10m users at a guess.
I think it is true that many people are updating their facebook status from their phones, but I would guess that many of those same people are still going to the website be it to look at photos they have recently been tagged in or play Farmville.
I think the original comment was saying that many people strictly use twitter from their phone or third-party app. There isn't much on twitter that draws an established user to the website like there is with facebook.
That is exactly what I meant, and that was exactly my point. Twitter wants to become a service provider. It seems it doesn't care so much about you visiting the site as much as it cares about you using the service it provides.
How this translates into twitter making money, we don't know yet, but it seems like it is the direction they are going with Chirp( http://chirp.twitter.com/ ) and with talk of giving more developers access to the firehose.
That argument doesn't make sense to me - what if people adopt 3rd party Twitter clients faster than the rate of new signups? You would have a net loss in web traffic even if new-user growth was increasing.
http://siteanalytics.compete.com/seesmic.com+tweetdeck.com/