Origins
Release and relax are the same word. Both descend from Latin relaxāre — 'to loosen again', from re- ('back, again') and laxāre ('to loosen'). Release took the French road, arriving in the 13th century through Old French relaissier, disguised almost beyond recognition. Relax took the scholarly road, borrowed directly from Latin in the 15th century with its form intact.
The Latin laxus meant 'loose, slack, wide'. From it grew lax (loose in discipline), lace (originally a noose or snare — something looped loosely), and lease (to let go of property temporarily). All involve some form of loosening or letting go.
Development
Release entered English as a legal and physical term. You released a prisoner from bonds, released a debtor from obligation, released a hawk from the fist. The film and music industry's use — releasing an album, a press release — is a 20th-century extension: sending something out into the world, loosening your hold on it.
The physical image at the core of the word has never changed. Whether you release a hostage, release tension, or release a new product, the underlying action is the same: you had a grip on something, and you opened your hand.