It could be that the the bride's father had died. There were no 'rules' as to what to put in that box. There are several points of view: if the father had died, therefore there was no father and he didn't have an occupation; or, there was a father, he did have a name, and an occupation when alive. I have two sisters in my tree, marrying just a few years apart, one left the boxes blank, the other filled them in. The most helpful state the father's name and add (deceased), and include the occupation, perhaps with (retired) if that was the case [that's what my OH did on our marriage certificate].
As to illegitimacy and adoption, the “father's name” may be the adopted father, or just the father-figure. In short, no guarantee of anything, unfortunately.