The Search count is the number of times a query has been searched. Search counts in Analytics are aggregated, whereas search requests refer to unaggregated search API calls made to the search engine for each keystroke during a search. For example, if users type "key," it will send search requests for "k," "ke," and "key," but only "key" will be used as a search in Analytics.
Tracked search count refers to the number of searches in which you include clickAnalytics:true in the query request. These searches are then forwarded to your Click and Conversion Analytics. If no searches are tracked, this means that you have not reported any searches to your click and conversion analytics.