This type includes audits by your company employees, consultants and contractors.
External
Supplier Audit
Second Party
This is where: 1. Customer employee(s) audit your company or where 2. Your employee(s) audit a company which supplies your company with a product or service.
Independent Organization
Third Party - Registrar
A customer wants an audit of your company but wants your company to pay for it.
This type of audit is described as independent. In QS-9000 (now IATF 16949) this is not really the case.
ISO 19011 - Quality and Environmental Management Systems Auditing Forum Discussions