Are my pages being shown 1 time with AdSense, and 9 times without?
Uh, the impressions are times your title and description showed in the SERPs AFAIK... So, I don't know how AdSense would have any correlation?
13% click through would mean your page showed 100 times in the SERPs and got 13 clicks, which seems to match your AdSense 10% number fairly closely...
Some of the accuracy would probably depend on when/what they count as an impression too... If it's while people are typing in the search box with instant on, then I could see where you could easily have 4 or 5 impressions before a search is even completed.
Maybe I'm misunderstanding something in your post?
The number of clicks reported is 29 times actual.
Not sure on this one, but some of that could be misreporting, and what you consider to be actual v. what they consider to be a click... Some of it could be those who surf with JS off, possibly new v. repeat visitors.
I wouldn't expect anything except 'close guesses' from stats ever.
I have sites with GA on them and register more sales than GA tracks, why? Maybe people don't make it to the thank you page, maybe the JS doesn't register before they close the thank you page, if there's more 'sales' in GA than are actual, maybe someone clicked refresh on the thank you page.
If your GWT account is off by a factor of 10, then delete a 0 from the end and work with the percentages... They're site: count has been off by that at some times previously, and if you code much at all you know it's an easy mistake to make, but finding and fixing it is fairly low on the priority list, because it's only possibly a big deal to a webmaster and fixing it doesn't make you a dime... I'd cut 'em a bit of slack on this one, especially if it's as simple as removing a 0 from the end of the number to get what you are thinking is correct.
If your site is slow or somehow doesn't load then you got a click from Google, but no visit. A short time ago ATT had a routing issue and none of my sites would load for certain parts of the country... Google sent me clicks, but I didn't get any visits. They're numbers aren't wrong, and neither are my stats, but they don't match...
[edited by: TheMadScientist at 5:27 am (utc) on Feb 8, 2011]