Inquiry, inquisition, investigation, inquest, probe, research all mean a search for truth, knowledge, or information.
Inquiry is the most general of these terms, applicable to such search regardless of the means (as questioning, observation, or experimentation) used or of the end in view.
Inquisition ordinarily carries heightened implications of searchingness and of penetration far below the surface to uncover what is concealed or withheld. The term, however, is chiefly applied to a judicial inquiry aiming to unearth facts or conditions to support suspicions or charges; probably from its historical application to the ruthless ferreting out of heretics or heresy especially in the late Middle Ages and in the Reformation period, the term generally connotes relentless pursuit of a clue or of a suspect, and sometimes merciless and rigorous persecution.
Investigation applies to an inquiry which has for its aim the uncovering of the facts and the establishment of the truth. In distinctive use it implies a systematic tracking down of something that one hopes to discover or needs to know.
Inquest applies chiefly to a judicial or official inquiry or examination especially before a jury, and specifically to one conducted by a coroner and jury in order to determine the cause of a death. In more general use, the term usually applies to an investigation that has some of the characteristics of a coroner’s inquest (as the exploration of the grounds for an accusation or suspicion in relation to some disastrous or troubling event).
Probe applies to an investigation that searches deeply and extensively with the intent to determine the presence or absence of wrongdoing; it suggests methods of exploration comparable to a surgeon’s probing for a bullet.
Research applies chiefly to an inquiry or investigation which requires prolonged and careful study, especially of actual conditions or of primary sources of information. It is especially applicable to scholarly and creative inquiries or investigations (as by scientists, historians, or linguists) especially for the sake of uncovering new knowledge, of getting at the facts when these are not known, or of discovering laws of nature, but it may sometimes be used for a study leading to the writing of a résumé of facts or laws already known or even for quite casual or trivial investigations.