Hi Miki
Those checkboxes actually influence the filter only. You can use them to let the Translator tool display strings from various versions. Then every row in the table is associated with one particular string at one particular version (see the first row in the table). The translation is then staged for the given row's version.
So no, there is nothing happening automatically between those versions. The Merge tool is currently the way how to copy strings from branch to another.
Hope this makes it clearer.