Before revision:  The first one is a predictor-corrector method that belongs to the family of flux-corrected transport (FCT) algorithms. The second approach constrains the antidiffusive part of a high-order target scheme using a new globalized monolithic convex (GMC) limiter. The flux-corrected approximations are BP under the time step restriction of the forward Euler method in the explicit case and without any time step restrictions in the implicit case. The FCT and GMC limiters can be applied to antidiffusive fluxes of intermediate RK stages and/or of the final solution update.
After revision:  The first one is a predictor-corrector method that belongs to the family of flux-corrected transport (FCT) algorithm but is applicable to spatial semi-discretizations and ensures the BP property of the fully discrete scheme for strong stability preserving (SSP) Runge-Kutta time discretizations. To circumvent the order barrier for SSP time integrators, we constrain the intermediate stages and/or of the final solution update.