Anyways the difference in tracking would be due to these are two separate tracking programs run by two separate companies. For example if your directly linking your Adwords ads to the affiliate url then its impossible for there to ever be any impressions. The impressions could be coming from when you look at the ad or when you where building the ad or from some other place you've placed the ad.
Now you might want to review the advertiser tos that your promoting under Adwords. They might not allow for direct linking to there site without someone seeing their banner or text ad that they've created.
But as for the difference in tracking each program tracks differently, so it’s really impossible to tell why, but as long as the links are working there shouldn’t be any problems.
It all comes down to a technical "opinion" of uniqueness.
It appears Adwords doesn't try too hard to filter out "duplicate" clicks, so affiliate programs may show fewer clicks than Adwords does.
These are just possible scenarios.
The impression count on Partner Gateway and many other affiliate programs/networks is based on their tracking a tiny 1 pixel image that is served by them and requested whenever your page is viewed.
You may have noticed that your affiliate code generally consists of at least two HTML statements, even when you are only building a text ad. One of the statements goes out to the affiliate network and requests an image where the code ends like this:
BORDER="0" WIDTH="1" HEIGHT="1" NOSAVE
It also sends information to the server about your affiliate code and what product you are advertising.
You may have noticed this tiny little 'dot' when you place their affiliate code on a website.
Of course, when you submit a text ad to AdWords, you cannot include this tiny "picture", so therefore your impressions are not measured properly. It is NOT mandatory that you use the 1x1 image, but it is the only way to gauge your impressions through the affiliate's tracking interface. Therefore in this case, you must go by the Google impression count.
The difference between the clickthroughs in AdWords vs. Partner Gateway could be a result of people clicking your adword, but not waiting for your affiliate ad page to load or it didn't load due to some issue at the affiliate's end. That stinks, but you still get charged by AdWords for the click.
The fact that you got any impressions from Partner Gateway suggests that either your ad is showing somewhere else other than AdWords (a link on another web site you have) or could have happened while you were testing the code.
Hope that helps,
patient2all