This item needs to be clarified. What is meant by the term "services"?
This subject could be divided into multiple components: API Structure, Response Bodies, Requests, and Documentation.
There is a difference between standards and specifications. The former is commonly defined as a set of rules that must be adhered to in order to earn compliance. The latter is more often related to a series of best practices that guide the design and structural style of the API.
Also, several standards and specifications may go into an end product. I use up to 6 for any given response body.
Here are a couple:
JSON-LD
Hydra
HATEOS
JSON:API
OGC API
HAL
Then there are the namespaces that provide vocabulary.
Schema.org
FOAF
DCAT
AC
SKOS
DWC