8 mm is 0.0025" (2,5 thou) larger than 5/16".
An 8 mm dia shaft will normally fit through a drilled 5/16" hole,
A 5/16" pin would normally fit into a hole drilled to a 5/16" clearance to give a running fit, so an 8 mm hole for a 5/16" moving pin will be just fine, but an 8 mm pin would fit OK under normal workshop tolerances.