Intelligence service is anything in the service of intelligence, or that serves intelligence—obviously.
Means of information gathering are both overt and covert and may include espionage, communication interception, cryptanalysis, cooperation with other institutions, and evaluation of public sources. The assembly and propagation of this information is known as intelligence analysis or intelligence assessment.
E.g. the Central Intelligence Agency; the Komitet Gosudarstvennoy Bezopasnosti (KGB). The George Bush Center for Intelligence is the headquarters of the Central Intelligence Agency. A 1983 Time magazine article reported that the KGB is the world's most effective information-gathering organization.
There is a distinction between "security intelligence" and "foreign intelligence". Security intelligence pertains to domestic threats (e.g., terrorism, espionage). Foreign intelligence involves information collection relating to the political, or economic activities of foreign states. An SIA is a State Intelligence Agency responsible for the collection, analysis, and exploitation of information in support of law enforcement, national security, military, and foreign policy objectives.
State Intelligence Agency agents are also known as servitors, servicemen or assets.
Two interconnected arguments can be offered about modern and early modern intelligence. The first challenges a common historical assumption that is clearly stated in R. Harris Smith's history of the OSS: "[The] R&A [Branch was the first concentrated effort on the part of any world power to apply the talent of its academic community to official analysis of foreign affairs."7 I want rather to suggest that precedents for the intelligence activities of Professors Read, Notestein, and Curtiss are to be found in the 16th- and 17th-century England they studied. Indeed, one can and should go much further back: Smith's claim seems especially shortsighted in light of David McMullen's work on official scholarly agencies in 7th- to 10th-century China.8