The tee_internal_core_api describes services that are provided to Trusted Applications. libutee is a library that implements this API.
libutee is a static library the Trusted Applications shall statically link against. Trusted Applications do execute in non-privileged secure userspace and libutee also aims at being executed in the non-privileged secure userspace.
Some services for this API are fully statically implemented inside the libutee library while some services for the API are implemented inside the OP-TEE core (privileged level) and libutee calls such services through system calls.
Now deprecated, used to provide the BigNum library in OP-TEE.