I was searching for the Esperanto word for stepfather, and I found two words, vicpatro and duonpatro. Are there any differences, in connotation or otherwise, between these two words? If they are simple synonyms, is one more common than the other? Dankon.
To your list you can also add stifpatro, which you'll find in at least a few dictionaries, but is far less common than the other two.
According to PIV:
Vic- la pure nominalan parencecon inter la gefiloj el unua edziĝo de unu membro de edzoparo k la gefiloj el unua edziĝo de la alia membro:
Duon- de parenceco inter la infanoj de unua edziĝo k la dua edzino de ilia patro (resp. la dua edzo de ilia patrino) aŭ inter tiuj infanoj k la infanoj de tiu dua edziĝo
The take-away here is that vic- has to do with non-blood relationships. Duon, on the other hand, can include both blood and non-blood relationships in blended families.
PIV doesn't seem to allow for vicpatro - but for sure it's a real word in actual use. (In fact, however, duonpatro is more common.) There is no difference in meaning.
So duonfrato appears to be ambiguous, since it includes half-brothers and step brother. Duonpatro however is not ambiguous because there's only one kind of duonpatro -- that is, a step father by marriage.
The question at this point, given that vicfrato is a step brother, and duonfrato is either a half brother or a step brother, how do you say simply "step brother." This is why stif- was proposed, but it seems that the semantic space is firmly taken up by vic- and duon- and so it isn't widely used.