Both the 1913 Picatinny rail and the Weaver mount have the same basic cross section.
However, the Picatinny spec calls for evenly-spaced cross-slots (recoil grooves) of a specific shape (square) and spacing. Not all Weaver mounts are built to this portion of the spec. Some have half-round slots, which may or may not be evenly spaced.
Therefore a Weaver ring will normally always fit a Pic rail but not all devices fitted with Picatinny rail attachments will fit all Weaver mounts.
This image shows the specifics of the Picatinny rail recoil grooves.
A glance at any Weaver mount will show the differences.