The number of search queries per search term as well as the total number of billed queries may differ between the Findologic customer account/invoice and Google Analytics.
The reasons for this are listed below:
Findologic counts each search query individually, even if a user searches several times for the same search term. Google Analytics, on the other hand, only evaluates the unique search queries per keyword/visit to the website.
In Findologic's billing, clicks on paginators (= scrolling between search result pages) and on filters count as queries. Google Analytics counts only the superordinate search query as a single search query.
At Findologic, tracking takes place on the server. Google Analytics tracks search queries via JavaScript. This can lead to situations in which search queries from users who have JavaScript deactivated or have made certain other privacy settings in their browser are tracked by Findologic, but not by Google Analytics.
See also the FAQ article on this topic: What is considered a billable search query?