Terminology for secret sharing? 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?
I believe there is strong enough precedence for using the term threshold decryption for the second. 

The abstract of this paper states:


  A threshold decryption scheme is a multi-party public key cryptosystem that allows any sufficiently large subset of participants to decrypt a ciphertext, but disallows the decryption otherwise.


Sounds to me like what you are talking about. A search for "threshold decryption" turns up plenty of hits too.