Hide, conceal, screen, secrete, cache, bury, ensconce are comparable when meaning to withdraw or to withhold from sight or observation. Hide , the general term, and conceal are often interchangeable.
But hide may or may not suggest intent or a putting into a place out of the range of others' sight.
Conceal, on the other hand, more often implies intention or effective hiding or a refusal to divulge.
Screen implies a hiding or concealment of someone or something in danger of being seen or known by interposing between him or it and others something (as a screen or curtain) which shelters and prevents discovery.
Secrete implies a depositing, often by stealth, in a place screened from view or unknown to others.
Cache implies an even more carefully chosen hiding place than secrete, for it usually implies protection from thieves or from the elements; sometimes the notion of secure storage more or less completely obscures that of concealment.
Bury implies a covering with or a submerging in something that hides or conceals or serves as a hiding place.
Ensconce in the relevant sense implies concealment especially in a raised or enclosed place.