Publishing marks are marks which solely change how publishing works. These marks always appear blue, because they never appear in the published score. These marks do not alter playback or MIDI exporting in any fashion. Add publishing marks the same way you would add a standalone mark.
Bar links added between bars forces those two bars to always appear on the same row. That is, two bars which are linked will never appear on different rows or different pages. Linking very long bars or a large number of bars together can prevent publishing from completing if the linked bars are wider than the page.
Line breaks force two bars to appear on different rows during publishing. That is, two bars which have a line break between them will always appear on different rows or different pages. If you wish to have two separate pieces of music published together, use sections instead.