In the latest Eleison Comments Bishop Williamson states the following
“One needs to be very careful with words, because words are the handle of our mind upon things, and things are the stuff of everyday life. Therefore upon words depends how we will lead our lives. At the flagship parish church of the Society of St Pius X in Paris, France, there is a Society priest taking due care of words. Fr Gabriel Billecocq wrote in last month’s issue (#333) of the parish’s monthly magazine Le Chardonnet an article entitled “Did you say ‘official Church’?.” In it he never once mentions Society Headquarters in Menzingen, Switzerland, but he does complain of the “wish” coming from somewhere, presumably on high, that the words “Conciliar Church” should always be replaced by the words “official Church.” And he is right, because the words “Conciliar Church” are perfectly clear, whereas the words “official Church” are not clear, but ambiguous.
For on the one hand “Conciliar Church” signifies clearly that large part of today’s Church which is more or less poisoned with the errors of the Second Vatican Council. Those errors consist essentially in the re-centring upon man of the Church which should be centred on God. On the other hand “official Church” is an expression with two possible meanings. Eitherit can mean the Church officially instituted by Christ and officially brought to us down the ages by the succession of Popes, and to that “official Church” no Catholic can object, on the contrary. Or “official Church” can be taken to mean that mass of the Church’s officials devoted to Vatican II who for the last half-century have been using their official power in Rome to inflict upon Catholics the Conciliar errors, and to this “official Church” no Catholic can not object. Therefore “Conciliar Church” expresses something automatically bad, while “official Church” expresses something good or bad, depending upon which of its two meanings it is being given. Therefore to replace “Conciliar Church” by “official church” is to replace clarity by confusion, and it also stops Catholics from referring to the evil of Vatican II.” (end quote)
Here is a recent article from the Dominicans of Avrille reminding us of the (conciliar) terms origins and the reason for its use.