Relationship between the word sodium and the word soda

Solution 1:

The word sodium is derived from the word soda.

Soda + ium -> sodium

(-ium is a suffix that forms names of metallic elements.)

Sodium: metallic alkaline element, 1807, coined by English chemist Humphry Davy from soda; so called because the element was isolated from caustic soda (sodium hydroxide). The chemical symbol Na is from natrium, alternative name for the element proposed by Berzelius from natron, a name of a type of soda - (Etymonline)

Soda: late 15c., "sodium carbonate," an alkaline substance extracted from certain ashes (now made artificially), from Italian sida (or Medieval Latin soda) "a kind of saltwort," from which soda was obtained, of uncertain origin. Perhaps it is from a Catalan sosa, attested from late 13c., of uncertain origin. Proposed Arabic sources in a name of a variety of saltwort have not been attested and that theory is no longer considered valid. Another theory, considered far-fetched in some quarters, traces it to Medieval Latin sodanum "a headache remedy," ultimately from Arabic suda "splitting headache."

Soda is found naturally in alkaline lakes, in deposits where such lakes have dried, and from ash produced by burning various seaside plants. A major trading commodity in the medieval Mediterranean, since commercial manufacture of it began in France in late 18c., these other sources have been abandoned. Washing soda (sodium carbonate) is commonly distinguished from baking soda (sodium bicarbonate). A soda-cracker (1863) has baking soda as an ingredient - (Etymonline)

Solution 2:

Soda comes from the Arabic word 'saltwort' and sodium (coined in 1807 by Humphry Davy) is a direct derivative of soda.