A more thorough explanation:

Tertium quid is a Latin term used in Scots law to describe a third thing that has qualities distinct from the prior two components.

For example, if two liquids are mixed together and the resulting mixture has different properties than either of the original liquids, it is considered a tertium quid.

Tertius gaudens is another Latin term that means "a rejoicing third." It refers to a third party who benefits when two others are in dispute.

For example, if two companies are in a legal battle and a third company profits from the situation, that third company is a tertius gaudens.