Origins
The word 'shore' entered English during the Middle English period, appearing in texts from around 1300. Its immediate source is Middle Dutch or Middle Low German 'schore' (shore, foreland), which is likely from Proto-Germanic *skurō, possibly connected to PIE *sker- (to cut, to shear). If this derivation is correct, a shore is etymologically 'cut land' — the edge where the sea has carved into the continent.
The PIE root *sker- is one of the most productive roots in the Indo-European family. From it descend 'shear' (to cut), 'share' (originally a ploughshare — a cutting blade), 'short' (cut off, curtailed), 'shirt' and 'skirt' (cut garments — these two words are doublets, the same Germanic word borrowed once through Old English and once through Old Norse), 'scar' (a mark left by cutting), 'score' (a scratch, a tally mark cut into wood), and 'skerry' (a small rocky island, from Old Norse 'sker,' a rock cut off from the mainland). The connection between all these words is the concept of separation by cutting.
Before 'shore' entered the language, Old English used 'strand' (beach, shore — still preserved in 'the Strand' in London, originally the bank of the Thames) and 'staþ' (shore, riverbank — surviving in place names like Hampstead and Armstead). The word 'beach' (originally meaning 'pebbles, shingle') did not acquire its modern sense of 'sandy shore' until the 16th century. 'Coast' (from Latin 'costa,' rib, side) arrived via Old French after the Norman Conquest. English thus accumulated four near-synonyms for the water's edge — shore, strand, beach, coast — each from a different source and each with slightly different connotations.
Development
There is a homonym worth distinguishing: 'shore' meaning 'a prop or support' (as in 'to shore up a wall') is a separate word, from Middle Dutch or Middle Low German 'schore' (a prop), possibly from a different semantic development of the same root — a cut timber used as a brace. The two words have been confused and may have influenced each other's development.
The compound 'offshore' (away from the shore, at sea) dates to the 17th century and has become a major term in modern finance ('offshore banking,' 'offshore accounts') and energy ('offshore drilling,' 'offshore wind'). 'Ashore' (on the shore, to the shore) preserves the older directional sense. 'Shoreline' is a 19th-century compound that has become the standard geographical and ecological term for the boundary between land and water.
In legal English, 'shore' has a precise technical meaning: the land between the ordinary high-water mark and the low-water mark — the intertidal zone. This narrow strip has been the subject of extensive property-law disputes throughout English and American legal history, as its ownership determines fishing rights, access to the sea, and (in modern times) rights to mineral resources beneath the seabed.