Phylogenetic algorithms: How to interpret multiple ML trees from the same dataset?
In short, you have chosen two examples that do not use maximum likelihood as you know it in other contexts. In most statistical contexts, the ML is a single number which can be calculated analytically, so it it always the same for a given data set. This is not the case for either MrBayes or RAxML but for different reasons.

MrBayes

The likelihood criterion in MrBayes is the marginal likelihood of the posterior, given effectively the data conditioned on the priors. This likelihood comes from a stochastic MCMC sampling of the parameter space. If all is well behaved, then the chains and/or runs will converge in the same general location. But then the different possible topologies need to be summarized in some way.

RAxML

RAxML generates essentially random starting trees by random sequence additions to build up trees. The subtrees are then rearranged to find a "best" tree. Again, different starting points may lead to different best trees. But if all goes well, analyses will end up with the same tree. This process is described in this chapter.

In both cases, if you start in a different place, you may end up in a different place. There may be many trees that are, within some criterion, equally likely. If you are familiar with parsimony methods, the analogy is that of multiple equally parsimonious trees.