Both words refer to a boundary where a surface or area ends. An edge is any line that bounds an area—the eastern edge of the city; trim the edges of the paper, and it usually functions like a line, without width, that divides one area from another. A periphery, which is a boundary all the way around a surface or area, is less exactly located than an edge and more like a space on either side: Set up the tables around the periphery of the room; countries along the western periphery of China. Periphery is frequently used of tracts or lots of land: the airport’s periphery; urban periphery. 

Hidden is the past participle of hide, as in, I’ve hidden the presents, but also an adjective often used with abstract nouns to suggest something present but not apparent or not perceivable: hidden talent; hidden meaning. Latent, which derives from a Latin verb meaning “to lie hidden,” can be a strong synonym for hidden. Latent refers to a power, ability, or emotion that is present as a potential, but is not yet apparent, fully developed, or openly expressed. A talent can lie or remain latent, hidden even from the possessor of it, if there has been no opportunity to develop or use it. A perceptive therapist might observe that a client’s frequent use of sarcasm reveals latent anger.

Both adjectives describe things that happen infrequently and not at regular intervals. Occasional refers to things that occur once in a while: occasional trips home; have the occasional drink. Occasional can have the effect of downplaying—both “casual” and occasional come from a Latin verb meaning “fall” or “befall,” that is, happen by chance. Sporadic’s descent from a Greek word for “seed” or “sowing,” and hence “scattered,” suggests things falling where or when they may. Sporadic emphasizes irregularity and is often paired with negative adjectives like inconsistent, unpredictable, and haphazard. In some contexts it implies that ideally things would be more frequent and consistent: sporadic efforts; sporadic attendance. Sporadic also tends to be used with explosive occurrences: sporadic outbursts; sporadic gunfire; sporadic violence.