The problem is that none of the absolute terminology is one hundred percent accurate. For me, at least, it breaks down like this:
Assassination doesn't really work in any way, as it is suggestive of something that did not happen
Execution is a fitting term applied to Nicholas-it was in the middle of the revolution, it was a political act, it was carried out by revolutionaries in a direct effort to achieve both vengeance AND to remove any possibility that he could return to the throne, and it followed considerable meetings in which it was discussed-no matter if the outcome of those meetings was largely determined in advance.
This same principle applies perhaps to Alexei-as heir to the throne, he represented the old regime and a continued threat, and whatever political principles infused the Russian Revolution they certainly took into account the desire to erase the old regime and the possibility of its return.
The "execution" argument applies in somewhat the same way to Alexandra, though less than with her son and certainly less than with her husband. She was perceived as having had a major political role in the ruin of the country, so as with Nicholas and Alexei her death combined both vengeance with political retribution. In her case she was probably killed more out of animosity as she certainly represented no threat that the dynasty would continue.
But then when you get to the Grand Duchess execution doesn't fit. It can be argued they fell in the same political retribution that ensnared their parents and brother, but I am personally more comfortable with simply asserting that Olga, Tatiana, Maria and Anastasia were murdered.
This take may offend some, but it's a more nuanced view of the factors that led to the events in the Ipatiev House. Nicholas, to me, was clearly executed, and I think this is also the most correct way to describe the death of Alexei and, less certainly, that of Alexandra. But the four Grand Duchesses would have been murdered since their deaths served no political purpose