If you are tracking results (goals and/or e-commerce revenue) you will probably notice some difference in results from other tracking mechanisms such as Google Adwords or third-party tracking software. If all visitors converted on the first visit, results would be more consistent, but unfortunately people frequently visit sites multiple times before converting.
Here are two reasons that you will see different results:
1. Google Adwords may not record multiple clicks on the same ad. Analytics will record each visit. Third party tracking software may track unique visits, so that mulitple visits are not shown.
2. Google Adwords sets a 30 day cookie on the browser. Therefore any conversion from this visitor within 30 days will be counted as an Adwords sale, regardless of the source of the visitor when the conversion was made. Google Analytics sets a 60 day cookie, but the cookie is overriden every time the visitor returns, unless the visitor enters the url directly. Third party software also usually cookies the browser. This may range from a temporary cookie that credits any returning visitor for a short period, like 30 days, to a permanent cookie that remains until cache and cookies are cleared in the pc.
Of course, there’s no right way. But it seems that the more likely the visitor is to convert on the first visit, the more valid your Google Analytics data will be. If it’s important to measure the original source from visitors who are likely to visit multiple times, then third-party software might provide better results.