Quick answer: a strand is a group of wires laid together; wire rope is an assembly of strands laid around a core. “Cable” is a broad commercial term and may refer to either. For procurement, specify construction such as 1×19, 7×7 or 7×19 instead of relying on the word cable.
1×7 and 1×19 constructions are relatively stiff and suit straight tension members, guying and standing rigging where little bending is expected. They are not interchangeable with flexible running rope.
7×7 offers moderate flexibility, while 7×19 uses more, finer wires for greater bending flexibility. Larger multi-strand constructions may be used for lifting or industrial motion, subject to the applicable standard and design.
The termination and smallest bend radius can control system life. Never substitute a flexible cable for a structural strand, or the reverse, from diameter alone.
Write the construction explicitly on the RFQ and drawing. Include lay direction, core, lubrication, coating, cut length and end fittings. Review stainless steel wire rope constructions for available selection paths.