Refers to a national legislative body as a whole. In Japan, 国会 is more common for the Diet, but 議院 is used in formal contexts and compound terms.
The role of parliament is to enact laws.
Refers to one of the houses within a bicameral legislature, such as the House of Representatives or the House of Councillors.
Japan's parliament consists of two houses: the House of Representatives and the House of Councillors.
The new bill was deliberated in the chamber.
He serves as the President of the House of Councillors.
The bill was passed by both houses.
議会 is a general term for any legislative assembly (national or local), whereas 議院 specifically denotes a chamber of Japan's bicameral Diet.
議院 (a house/chamber of parliament) and 議員 (a member of parliament) are pronounced identically but refer to completely different things.
Compound of 議 (deliberation) and 院 (institution, house).