No all metal do not rust. Rust is a specific term used for corrosion of iron. However, corrosion is more generic term which is used for all metals. Metal like Au(gold) , Pt(platinum), Pd(palladium), etc. does not corrode and hence termed as noble metals. Elements like Al and Zn which undergoes corrosion but the corrosive layer form does not allows further corrosion of Al and Zn.