When people talk about clashing colours, they generally mean that the colours compete with each other, leading to a chaotic result. There's no clear definition of what makes a clashing colour combination. Some refer to colours that are opposite each other on the colour wheel, as 'contrasting' or 'clashing colours', but as we've seen above, this is totally incorrect. 'Opposite' colours are actually complementary and often go very well together.
Rather, clashing colours are colours that have unrelated resonance, which is more to do with the intensity and and undertone of the shade than the colour's place on the colour wheel. For example, if you mix a warm shade with a cool shade, or a muted colour with a bright colour, it could create a jarring effect. But there is no rule. Muted variations on a colour are often used with brighter shades for certain effects.