Yes, candid and candidate are cognate. It’s ironic, of course, that a word referring to forthrightness and honesty is the basis of a noun referring to someone who stands for political office.
Candid is from the Latin term candidum, which means not only “sincere” and “upright” but also “white” and “pure.” Candidatus, the Latin predecessor of candidate, means “white robed,” and alludes to the fact that those campaigning for public office in ancient Rome wore white.
Candid also means “blunt” or “frank” but also came, by extension, to mean “spontaneous,” as in referring to someone photographed in a candid pose rather than a prepared one. Meanwhile, candidate now can also refer to an applicant for any position, whether in a political context or otherwise, or to someone vying for an award or one who meets, or is on track to meet, all the requirements for something.
Synonyms for candidate include applicant, referring to someone who applies or asks for something, from the Latin verb applicare, meaning “fold to.” (The second syllable of apply is has the same as the word ply.) Another is aspirant, meaning “someone who tries to be or do something,” derived from the Latin verb aspirare, meaning “breathe on.”
Campaigner, which refers to someone who embarks on a political campaign to seek office, derives ultimately from the Latin term campania, meaning “level ground” and referring to the type of terrain most easily traversed by an army on the march; campaign originally referred to a series of battles waged to produce a desired strategic outcome. Contender, meanwhile, refers to someone who tries to win something, especially someone with a strong possibility of victory; the root word, contend, stems from the Latin verb contendere, meaning “stretch with” in the sense of a competitor who physically strives to win.
Nominee, from the Latin verb nominare, meaning “name,” pertains to someone who has been chosen to represent a political party for a specific office or someone who is being considered for a position. Prospect denotes someone likely to win or be chosen; the word, from the Latin verb prospicere, meaning “look forward,” also refers in general to anticipation or possibility, or to a lookout or a scene or a survey.