It does appear that "multi-level selection" is terminology that was invented to give group selection a face lift - and allow it to escape from an unglamorous past.
However, group selection is not more or less "multi-level" than kin selection is. The concepts of "relatedness" and "kin selection" can be applied at multiple levels too. One can meaningfully discuss the relatednes between cells in an ant, the relatedness between an ant and its sisters and the relatedness between entire colonies of ants. This has been understood since the 1970s and it can be seen as a result of the generality of the Price equation.
These days, group selection enthusiasts often prefer to use the "multi-level selection" terminology. This article is my explanation of why I rarely follow them - and why I think it is a confusing gambit. Kin selection is "multi-level" too. Using the term "multi-level selection" fails to distinguish between kin selection and group selection. It is true that kin selection and group selection are equivalent - in the sense that modern versions of these theories make the same predictions. However that doesn't mean that proponents use the same methodologies. These are still topics that are worth distinguishing between. The best way of doing that is, I think to use the terms "kin selection" and "group selection".