Improperly implemented conversion tracking snippet is a likely cause. For example, if a user reloads the thank you page, does that fire the conversion script more than once for the same session? That could cause the same conversion to be counted multiple times if not properly implemented.
Are you storing leads in a database, or are they simply sent to an email account? Email is not 100% reliable, I have seen instances where the emails failed to be delivered on occasion, which would account for a discrepancy.
Another thing I have seen is Adwords Conversion tracking being used simultaneously with Google Analytics accounts that are linked and set to import goal completions as conversions. That can lead to over-reported conversion numbers inside your AdWords account.
Yet another possibility is delayed reporting due to time differences in your AdWords account where a conversion in the last hours of the day gets reported on the following day’s reports.
Please rule those possibilities out, and if you are still having discrepancies let us know and we’ll try to help.