Different purpose
Maintenance exists to prevent breakdown and reduce downtime; its plan follows production needs. A periodic inspection verifies, against defined criteria and a defined method, that the equipment is safe to use. A crane may be greased and running, and that says nothing about whether its rope, brake and limit switch were examined.
Who may do it, and the record
Maintenance can be done by the organisation's own team. A periodic inspection is carried out by someone holding the competence defined for that equipment type, and the result is reported together with the measured values. The report does not end at "compliant": it states which criterion was met with which value, and if there is a non-conformity the equipment is taken out of service.
The intervals and the criteria themselves vary by country; Optifora builds the inspection calendar from the equipment type and from the regulation of the country the organisation operates in.