Primary sources are materials contemporaneous to the time you are researching, created by someone with first-hand experience of the phenomena that you are researching. Primary sources can come in any format, including newspaper articles, diaries, memoirs, letters, reports, scholarly articles, books (including works of fiction and non-fiction), films, artworks, laws, financial records, posters, photographs, and artifacts.
Archives are materials created or collected by people or organizations, in the course of their every-day activity, which are preserved because of their "enduring value" (Society of American Archivists). Another definition of archives: unique constellations of materials, collected and preserved because they contain important information and/or evidence of their creator's responsibilities and actions. All archival collections are comprised of primary sources, but not all primary sources are archival.
Because primary sources can come in any format, many databases and other places you would look for secondary sources are also good for finding primary sources. Examples of this include books in CLIO or HathiTrust and scholarly journal articles in JSTOR (which includes articles from the 19th century, helpful for researching the history of a given field or area of knowledge) or other databases. One way to find primary sources in these places is to limit by date to the period you're researching. Another is to use keywords (particularly in CLIO) such as memoir, autobiography, source*, documentary (which often refers to books of re-printed primary source materials), letters, etc.