The Berry mechanism refers to the facile interconversion of axial and equatorial ligand in  types of compounds, e.g. D3h-symmetric  (shown). Finally, in a formal sense, the term pseudorotation is intended to refer exclusively to dynamics in symmetrical molecules, though mechanisms of the same type are invoked for lower symmetry molecules as well.
The Berry mechanism pertains to the effortless interchange of axial and equatorial ligands in specific compound classes, like D3h-symmetric ones (as illustrated). In a formal context, pseudorotation is meant to exclusively denote dynamics within symmetrical molecules. Yet, analogous mechanisms are also applied for lower symmetry compounds.