Is there any connection to CohFTs as defined by Witten in his 1988 paper (via topological twist) and the CohFTs as defined by Kontsevich and Manin (in the context of Gromov-Witten theory of course).

I mean, is there a general definition of CohFT such that every simple (physics or maths) example such as Donaldson theory, Vafa-Witten theory, Gromov-Witten theory, Donaldson-Thomas theory, etc falls under this definition?