One is the international certificate, among which the more authoritative GIA certificate of the United States has diamonds, and most countries have appraisal institutions, such as Japan and South Africa.
The other is the domestic certificate, and the most authoritative one is the national inspection, which has set up offices in Shanghai, Shenzhen and Beijing. After that, every province has a provincial inspection, and generally there are subsidiaries established by the provincial land resources and geology bureau. These are all qualified, such as provincial stations and jewelry associations.
Another kind is relatively individual. Some merchants will issue their own certificates, generally the certification marks are unqualified, but most buyers only care about whether there is a certificate or not, and do not pay attention to the issuer of the certificate, which has caused some unnecessary risks to themselves.
This is a personal induction, or it may not be complete, for reference only.