I was wondering what's the difference between threshold signatures and multisignatures. In what respects do they differ? For example, is n-out-of-n threshold signature, just a multisignature?
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Threshold signatures do not enforce accountability meaning a t-out-of-n threshold signature does not tell the verifier which $t$ of the $n$ signers created the signature. Multisignatures enforce accountability as the verifier learns which t signers created the signature. There does not need to be a threshold for multi-signatures.
But n-out-of-n threshold signature should give same properties as an n-multisignature.
As an example, consider BLS signatures. You can have a 3-of-5 threshold signature without learning which 3 signers created it but if you had a multisignature from 3 signers, you need to know which 3 signers created the signature (so you add their public keys). In fact a threshold signature by any 3 signers will have the same value but a multi-signature will have different values depending on which 3 signers were involved. You could create a multi-sig from 2 signers as well.
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1$\begingroup$ Small markdown hint: you need two end-of-lines to create a new section (which is preferred to just starting a new line, which can be done by adding two spaces before a single newline) $\endgroup$– Maarten Bodewes ♦Jan 24, 2020 at 18:21
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