A sub frame structurally includes "cross-members" but a cross member itself is not usually a sub-frame. That is, a sub-frame is typically a larger piece and one that will often be a cradle for the engine as well as provide attachment points for the suspension.

What else is a subframe called?

Secondary frame, supporting frame.

What is a subframe on a car?

The subframe is the structure below the frame that supports the axle, suspension and powertrain. For internal combustion engines, in the front, it is often referred as the engine cradle, or in some cases, the K-frame.