I'm not familiar with the details on the PROCESS macros, but I don't have access to the documentation for the PROCESS macro, but based on some logistic regression output from it I tracked down:
The -2LL value is -2 times the log-likelihood* for the final fitted logistic regression model, which would be somewhat analogous to a residual sum of squares for a linear model.
The ModelLL is the difference in -2 log-likelihoods between the final model and a "null" model, which typically is one with just an intercept (but in some contexts might be a model with a subset of the predictors from the full model), and under the null hypothesis that all predictors added in the larger model are 0 in the population, that's distributed as a chi-square with degrees of freedom equal to the number of additional parameters in the larger model. This is analogous to your F statistic from a linear model.
The McFadden pseudo-R^2 is the proportional reduction in -2 log-likelihood achieved by adding the additional parameters, or ModelLL/(-2LL+ModelLL), and in that sense is the most analogous of the pseudo-R^2 measures to the linear model R^2, but none of them is exactly analogous in all ways, which is why there are multiple ones given.
*The values given for -2 log-likelihoods are almost certainly technically -2 times the kernels of the binomial log-likelihoods rather than the full log-likelihoods, but in models with no duplicated covariate or predictor patterns these are the same, and it's more common just to use the kernel value and ignore the binomial constant that doesn't affect the maximum likelihood estimates. If you compare results from LOGISTIC REGRESSION in SPSS Statistics with results from NOMREG or GENLIN for the same binary logistic model, you might get values that differ by a constant unless you specify use of the kernel values in the latter two procedures, which use the full likelihood values by default, while LOGISTIC REGRESSION always reports values based on the kernel.