An equational clause is a °clause construction that puts two °nominals both of which are °definite in correspondence.
The definition is from Haspelmath (2025: 17). "Putting two nominals in correspondence" is a formulation chosen to be neutral between different readings such as characterizational and specificational. How to best describe the meanings of such sentences is not quite clear (cf. den Dikken & O'Neill 2017). Creissels et al. (2016: §4.2) use "identity predication" for equational clauses. ❡
Croft's (2022) use of "equational" is somewhat different, and perhaps more like Grammaticon's "tautotic".
equational (INF/CXN) = a type of identificational information packaging in which two referents that the hearer assumed were different individuals are asserted to be, in fact, one and the same individual; and the construction that expresses that information packaging. Example: in The Morning Star is the Evening Star, it is asserted that two celestial objects that were once thought to be distinct objects (and given distinct names) are one and the same, namely the planet Venus. (Section 10.1.2)