Your post did not provide enough information to pinpoint the exact reason you are seeing a difference, however, I will try to provide answers that help clarify the data and improve your testing methods.
First, I did not see where you mentioned certain specifics in how you set up the AdWords ad test:
- What keyword match type did you use for the keyword in your ad group? The keyword match type determines which keyword, or group of keywords, will trigger ad impressions. I assume you used the exact match only but did not see that indicated in your post.
- Did you turn off the AdWords stemming feature (close variants) in the advanced settings of the campaign? If you failed to perform this step then your ad will trigger impressions for a group of keywords, not just the keyword you were targeting, even if you had included a single exact match keyword. This would, in part, account for a higher level of impressions than you had expected to receive.
- Was your campaign budget unlimited? If not, that may have reduced impressions.
- Did you bid high enough to have a first-page listing for every possible impression? If your average ad position was not at or near 1.0 then the actual potential impressions may have been greater than what was recorded for your ad. Check the impression share stats to confirm that it was 100%.
Now, let’s talk about the AdWords Keyword Tool. This tool reports actual data, not an estimate as you seem to have implied. As always, past performance does not reliably predict future performance.
As others on this thread have pointed out, a 24-hour test cannot give you enough data to extrapolate an accurate estimate of monthly traffic. Most keyword traffic will vary a great deal based on the day of the week, and sometimes the day of the month. Anything less than a 2-week test would be highly unreliable.
Hopefully, this may give some clues as to why your test had a greater than expected variance for the data reported by the AdWords Keyword Tool.