This is like Copy Skin Weights for deformer and blend shape weights.
Select the source and destination deformers to copy.
If a blendShape is selected, you can select the blend shape target's weights to copy, or "Main deformer weights" to copy the main deformer weights.
If both the source and destination deformers are blendShapes, you can select "All (match by name)" in the source blend shape target, and all blend shape targets with matching names will have their weights copied. The deformer weights will also be copied. If this is selected, the blend shape target in the target deformer will be greyed out.
If more than one mesh is affected by either deformer, select which one to copy from the Shape dropdowns.
Click Apply.