The best answer I can give to this question is that eventually, every volcano does erupt from a mountain. However, there are plenty of volcanoes around the world that are not currently mountains. The best technical definition is “a mountain or hill, typically conical, having a crater or vent through which lava, rock fragments, hot vapor, and gases are being or have been erupted from the earth’s crust” from Google’s dictionary function.
So, it could be a hill or a mountain, but they must have a vent or crater for lava and other things to flow to the surface.
That is the crucial part of the definition. As the previous answer states, all volcanoes start as a vent or a crater. The debris is what creates the mountain around a volcano.