schooner n.

fore-and-aft rigged vessel, originally with but two masts, 1716, perhaps from a New England verb related to Scottish scon "to send over water, to skip stones." Skeat relates this dialectal verb to shunt. The spelling probably was influenced by Dutch, but Dutch schoener is a loan-word from English, as are German Schoner, French schooner, Swedish skonert. The type of ship itself is said to have been first built in Gloucester, Mass., shipyard.

The rig characteristic of a schooner has been defined as consisting essentially of two gaff sails, the after sail not being smaller than the fore, and a head sail set on a bowsprit. [OED]

Meaning "tall beer glass" is by 1879, of unknown origin or connection to the sailing ship word (the ships are not noted for their size); OED calls it a "fanciful use" of it.