What is the difference between Statutory Certificates, Trading Certificates, Mandatory certificates and Obligatory Certificates ?

There is one principle difference between Statutory certificates and Mandatory certificates.
Statutory certificates are required by law (Statute). Sailing a ship to the sea without any of these certificates will be like breaking the law.
Mandatory certificates are mandatory for a particular trade or for some other reasons. For example "Certificate of financial responsibility" (COFR) is mandatory for the vessel trading in US. For a Non-US flagged ship it is not statutory to have COFR but it is mandatory for entering and operating in US waters.
Mandatory certificates are also called obligatory certificates.
All the certificates that are required for uninterrupted trading of the vessel (Statutory and mandatory certificates) are called trading certificates.