A “multi-national” law department has lawyers based in more than one country. One country has the largest portion, and that country and location is thought of as headquarters. Many large US companies have multi-national law departments.
An “international” law department is multi-national, but some of its groups of lawyers are large and can stand on their own. Diageo’s law department is international.
A “global” law department is international, but the company has legitimate, powerful business units – and groups of lawyers supporting them, who often report to the head of the business – in more than one country. DeutscheBank’s legal department is global.
OK, if you disagree with my stab at a definition, let me know!