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.
See also the FAQ article on this topic: What is considered a billable search query?