To my understanding, there are two "approaches" to t out of n threshold encryption. In both of them, n shares are given to different shareholders, and at least t of them must agree to "proceed". "Proceed" can take two different meanings: either the shares are the input to derive a secret that can be used to perform a traditional decryption (e.g. Shamir) or the shareholders produce a partial encryption that can be put together to generate the decryption (e.g. Damgård-Jurik).
I have found the first scenario to be known as secret sharing, but I am looking for a term to describe the second approach unambiguously. Does such term exist?